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2026-01-01
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<p>Last updated on<strong>December 10, 2025</strong></p>
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<p>Last updated on<strong>December 10, 2025</strong></p>
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<p>Algebraic expressions are polynomials made up of variables and coefficients, and combined using arithmetic operations. Polynomials in one variable have the form axn, where a is a real number and n is a non-negative integer.</p>
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<p>Algebraic expressions are polynomials made up of variables and coefficients, and combined using arithmetic operations. Polynomials in one variable have the form axn, where a is a real number and n is a non-negative integer.</p>
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<h2>What are Polynomials in One Variable?</h2>
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<h2>What are Polynomials in One Variable?</h2>
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<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<p>Polynomials in one<a>variable</a>are<a>algebraic expressions</a>consisting<a>of</a><a>terms</a>with single variable and coefficients, combined using<a>arithmetic operations</a>. For example:</p>
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<p>Polynomials in one<a>variable</a>are<a>algebraic expressions</a>consisting<a>of</a><a>terms</a>with single variable and coefficients, combined using<a>arithmetic operations</a>. For example:</p>
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<p>x2 + 5x + 8</p>
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<p>x2 + 5x + 8</p>
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<p>2y3 + 5y2 + 9y + 3 </p>
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<p>2y3 + 5y2 + 9y + 3 </p>
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<p>The above examples have only one variable (‘x’ in the first example and ‘y’ in the second).</p>
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<p>The above examples have only one variable (‘x’ in the first example and ‘y’ in the second).</p>
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<h2>Classification of Polynomials in One Variable</h2>
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<h2>Classification of Polynomials in One Variable</h2>
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<p>Polynomials in one variable can be grouped into different types, depending on their degree. The degree of a<a>polynomial</a>is simply the highest<a>exponent</a>of the variable. Based on this, polynomials are usually divided into four main types: </p>
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<p>Polynomials in one variable can be grouped into different types, depending on their degree. The degree of a<a>polynomial</a>is simply the highest<a>exponent</a>of the variable. Based on this, polynomials are usually divided into four main types: </p>
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<ul><li>Zero or Constant Polynomial</li>
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<ul><li>Zero or Constant Polynomial</li>
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<li>Linear Polynomial</li>
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<li>Linear Polynomial</li>
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<li>Quadratic Polynomial</li>
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<li>Quadratic Polynomial</li>
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<li>Cubic Polynomial </li>
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<li>Cubic Polynomial </li>
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</ul><p><strong>Zero or Constant Polynomial:</strong>A zero or<a>constant polynomial</a>’s variable has no exponent, meaning its degree is 0. As a result, these polynomials only include constant terms. For example, 2x0 = 21 = 2.</p>
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</ul><p><strong>Zero or Constant Polynomial:</strong>A zero or<a>constant polynomial</a>’s variable has no exponent, meaning its degree is 0. As a result, these polynomials only include constant terms. For example, 2x0 = 21 = 2.</p>
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<p><strong>Linear Polynomial:</strong>The polynomials with 1 as the highest degree of the variable are the<a>linear polynomials</a>. For example, x + 2, 6x + 5. </p>
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<p><strong>Linear Polynomial:</strong>The polynomials with 1 as the highest degree of the variable are the<a>linear polynomials</a>. For example, x + 2, 6x + 5. </p>
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<p><strong>Quadratic Polynomial:</strong>Quadratic polynomials are the polynomials with the highest degree of 2. For example, 5x2 + 2x + 6, 6y2 + 5y + 1</p>
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<p><strong>Quadratic Polynomial:</strong>Quadratic polynomials are the polynomials with the highest degree of 2. For example, 5x2 + 2x + 6, 6y2 + 5y + 1</p>
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<p><strong>Cubic Polynomial:</strong>A<a>cubic polynomial</a>is one in which the highest degree of the polynomial is 3. For example, 5x3 + 2x2 + 8x + 7 </p>
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<p><strong>Cubic Polynomial:</strong>A<a>cubic polynomial</a>is one in which the highest degree of the polynomial is 3. For example, 5x3 + 2x2 + 8x + 7 </p>
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<h2>How to Solve Polynomials in One Variable?</h2>
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<h2>How to Solve Polynomials in One Variable?</h2>
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<p>Solving a polynomial is the process of finding the values of the variable that make the whole<a>expression</a>equal to zero. The solution of the polynomial is also known as roots or zeros of the polynomial. A polynomial of degree n can have up to n roots. So, linear polynomials have one root, quadratic polynomials have two roots and cubic polynomials have three roots. </p>
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<p>Solving a polynomial is the process of finding the values of the variable that make the whole<a>expression</a>equal to zero. The solution of the polynomial is also known as roots or zeros of the polynomial. A polynomial of degree n can have up to n roots. So, linear polynomials have one root, quadratic polynomials have two roots and cubic polynomials have three roots. </p>
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<p><strong>Solving Linear Polynomial in One Variable</strong> </p>
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<p><strong>Solving Linear Polynomial in One Variable</strong> </p>
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<p>The general form of a<a>linear polynomial</a>is ax + b = 0. Now let’s learn how to solve a linear polynomial, with an example:</p>
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<p>The general form of a<a>linear polynomial</a>is ax + b = 0. Now let’s learn how to solve a linear polynomial, with an example:</p>
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<p>3x - 6 = 0</p>
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<p>3x - 6 = 0</p>
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<p><strong>Step 1:</strong>To solve, isolate the term with the variable</p>
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<p><strong>Step 1:</strong>To solve, isolate the term with the variable</p>
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<p>3x = 6</p>
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<p>3x = 6</p>
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<p><strong>Step 2:</strong>Isolate the variable</p>
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<p><strong>Step 2:</strong>Isolate the variable</p>
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<p>x = 6/3</p>
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<p>x = 6/3</p>
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<p>x = 2</p>
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<p>x = 2</p>
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<h2>Solving Quadratic Polynomial in One Variable</h2>
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<h2>Solving Quadratic Polynomial in One Variable</h2>
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<ul><li>Factoring</li>
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<ul><li>Factoring</li>
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<li>Using quadratic<a>formula</a></li>
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<li>Using quadratic<a>formula</a></li>
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<li>Completing the<a>square</a></li>
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<li>Completing the<a>square</a></li>
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</ul><p><strong>Factoring:</strong>In the factoring method, the quadratic polynomial is expressed as a<a>product</a>of two<a>binomial</a>expressions. The general form of a quadratic<a>equation</a>is ax2 + bx + c = 0. To<a>factor</a>, we find two numbers whose product is equal to ac and sum is equal to b. </p>
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</ul><p><strong>Factoring:</strong>In the factoring method, the quadratic polynomial is expressed as a<a>product</a>of two<a>binomial</a>expressions. The general form of a quadratic<a>equation</a>is ax2 + bx + c = 0. To<a>factor</a>, we find two numbers whose product is equal to ac and sum is equal to b. </p>
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<p>For example, finding the root of x2 + 5x + 6 = 0</p>
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<p>For example, finding the root of x2 + 5x + 6 = 0</p>
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<p>Here, a = 1, b = 5, and c = 6</p>
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<p>Here, a = 1, b = 5, and c = 6</p>
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<p>Here the factors are 2 and 3, whose sum is 5 and product is 6</p>
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<p>Here the factors are 2 and 3, whose sum is 5 and product is 6</p>
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<p>So, x2 + 5x + 6 = (x + 2)(x + 3) = 0</p>
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<p>So, x2 + 5x + 6 = (x + 2)(x + 3) = 0</p>
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<p>x + 2 = 0 and x + 3 = 0</p>
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<p>x + 2 = 0 and x + 3 = 0</p>
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<p>x = -2 and x = -3</p>
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<p>x = -2 and x = -3</p>
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<p><strong>Using Quadratic Formula:</strong>The general form of a quadratic polynomial is ax2 + bx + c = 0, where a ≠ 0. The formula to find the value of x is</p>
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<p><strong>Using Quadratic Formula:</strong>The general form of a quadratic polynomial is ax2 + bx + c = 0, where a ≠ 0. The formula to find the value of x is</p>
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<p>For example, 2x2 - 4x - 6 = 0</p>
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<p>For example, 2x2 - 4x - 6 = 0</p>
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<p>Here, a = 2, b = -4 and c = -6</p>
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<p>Here, a = 2, b = -4 and c = -6</p>
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<p>x = 3 and x = -1</p>
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<p>x = 3 and x = -1</p>
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<p><strong>Solving Cubic Polynomial in One Variable</strong></p>
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<p><strong>Solving Cubic Polynomial in One Variable</strong></p>
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<p>The general form of a cubic equation is ax3 + bx2 + cx + d = 0, where a ≠ 0. To solve a cubic equation, follow these steps: </p>
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<p>The general form of a cubic equation is ax3 + bx2 + cx + d = 0, where a ≠ 0. To solve a cubic equation, follow these steps: </p>
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<p>For example, finding the value of x in</p>
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<p>For example, finding the value of x in</p>
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<p>Here, the equation is in standard form:</p>
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<p>Here, the equation is in standard form:</p>
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<p>If</p>
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<p>If</p>
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<p>So, x = 1 is a root</p>
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<p>So, x = 1 is a root</p>
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<p>Factoring:</p>
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<p>Factoring:</p>
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<p>Solving the quadratic equation:</p>
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<p>Solving the quadratic equation:</p>
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<p>So, x = 1, 2, 3</p>
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<p>So, x = 1, 2, 3</p>
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<h2>Tips and Tricks of Polynomials in One Variable</h2>
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<h2>Tips and Tricks of Polynomials in One Variable</h2>
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<p>Polynomials may look tricky, but they’re actually patterns made of<a>numbers</a>and variables. A polynomial in one variable means it has only one type of variable, like x or y. These handy tips and tricks will help you easily identify, simplify, and understand polynomials in one variable. </p>
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<p>Polynomials may look tricky, but they’re actually patterns made of<a>numbers</a>and variables. A polynomial in one variable means it has only one type of variable, like x or y. These handy tips and tricks will help you easily identify, simplify, and understand polynomials in one variable. </p>
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<ul><li>A polynomial in one variable means it has only one variable (like x, y, or z).</li>
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<ul><li>A polynomial in one variable means it has only one variable (like x, y, or z).</li>
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<li>The highest<a>power</a>of the variable tells you the degree of the polynomial.</li>
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<li>The highest<a>power</a>of the variable tells you the degree of the polynomial.</li>
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<li>Arrange terms from the highest power to lowest for clarity.</li>
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<li>Arrange terms from the highest power to lowest for clarity.</li>
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<li>Combine only terms with the same variable and power.</li>
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<li>Combine only terms with the same variable and power.</li>
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<li>The number before the variable is called the<a>coefficient</a>.</li>
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<li>The number before the variable is called the<a>coefficient</a>.</li>
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</ul><h2>Common Mistakes and How to Avoid Them in Polynomials in One Variable</h2>
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</ul><h2>Common Mistakes and How to Avoid Them in Polynomials in One Variable</h2>
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<p>When learning polynomials in one variable, students often get confused with the concept and make errors. Here are a few common mistakes that we can avoid in the future. </p>
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<p>When learning polynomials in one variable, students often get confused with the concept and make errors. Here are a few common mistakes that we can avoid in the future. </p>
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<h2>Real-World Applications of Polynomials in One Variable</h2>
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<h2>Real-World Applications of Polynomials in One Variable</h2>
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<p>Polynomials in one variable are useful in various fields, such as business, science, and engineering, for modeling situations, making predictions, and analyzing patterns. In this section, we will learn some real-world applications of polynomials. </p>
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<p>Polynomials in one variable are useful in various fields, such as business, science, and engineering, for modeling situations, making predictions, and analyzing patterns. In this section, we will learn some real-world applications of polynomials. </p>
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<ul><li>In physics, polynomials in one variable are used in modeling projectile motion. It helps to calculate the trajectory of a ball, a rocket, or a jet of water from a fountain. </li>
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<ul><li>In physics, polynomials in one variable are used in modeling projectile motion. It helps to calculate the trajectory of a ball, a rocket, or a jet of water from a fountain. </li>
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<li> In civil engineering, a polynomial in one variable is used to design roller coasters to ensure smooth and continuous curves to ensure a safe and exciting ride for riders. </li>
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<li> In civil engineering, a polynomial in one variable is used to design roller coasters to ensure smooth and continuous curves to ensure a safe and exciting ride for riders. </li>
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<li>In finance, to calculate the<a>compound interest</a>over several periods, financial planning, retirement saving projections, and loan calculations we use the polynomials in one variable. </li>
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<li>In finance, to calculate the<a>compound interest</a>over several periods, financial planning, retirement saving projections, and loan calculations we use the polynomials in one variable. </li>
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</ul><h3>Problem 1</h3>
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</ul><h3>Problem 1</h3>
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<p>Find the degree of polynomial 8x2 + 6x + 5x3 - 6</p>
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<p>Find the degree of polynomial 8x2 + 6x + 5x3 - 6</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The degree of a polynomial is 3 </p>
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<p>The degree of a polynomial is 3 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> The degree of a polynomial is based on the largest power of the variable. In this case, the highest power is 3, so the polynomial is of degree 3. </p>
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<p> The degree of a polynomial is based on the largest power of the variable. In this case, the highest power is 3, so the polynomial is of degree 3. </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>Identify the type of polynomial based on their degree: 5x^2 + 6x, x - 5</p>
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<p>Identify the type of polynomial based on their degree: 5x^2 + 6x, x - 5</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> Here, is a quadratic polynomial and x - 5 is a linear polynomial </p>
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<p> Here, is a quadratic polynomial and x - 5 is a linear polynomial </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> Based on the degree, the polynomials are classified into linear, quadratic, and zero degree polynomials. </p>
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<p> Based on the degree, the polynomials are classified into linear, quadratic, and zero degree polynomials. </p>
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<p>In , the highest degree of polynomial is 2, so it is a quadratic polynomial.</p>
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<p>In , the highest degree of polynomial is 2, so it is a quadratic polynomial.</p>
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<p>In x - 5, the highest degree of polynomial is 1, so it is a linear polynomial.</p>
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<p>In x - 5, the highest degree of polynomial is 1, so it is a linear polynomial.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>Find the root of the polynomial: 2x - 6</p>
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<p>Find the root of the polynomial: 2x - 6</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> x = 3 </p>
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<p> x = 3 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> Arranging the equation in general form ax + b = 0</p>
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<p> Arranging the equation in general form ax + b = 0</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>Which of the following are polynomials in one variable? 2x2 + 5x + 5xy 3y3 + 5y - 6y2 x + 2</p>
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<p>Which of the following are polynomials in one variable? 2x2 + 5x + 5xy 3y3 + 5y - 6y2 x + 2</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Here, and are polynomials in one variable. </p>
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<p>Here, and are polynomials in one variable. </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> The first expression, has two variables (x and y). Hence, it is not a polynomial in one variable. </p>
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<p> The first expression, has two variables (x and y). Hence, it is not a polynomial in one variable. </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Polynomials in One Variable</h2>
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<h2>FAQs on Polynomials in One Variable</h2>
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<h3>1.What is a polynomial in one variable?</h3>
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<h3>1.What is a polynomial in one variable?</h3>
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<p>An algebraic expression that contains only one variable is called a polynomial in one variable. </p>
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<p>An algebraic expression that contains only one variable is called a polynomial in one variable. </p>
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<h3>2.List a few examples of polynomials in one variable?</h3>
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<h3>2.List a few examples of polynomials in one variable?</h3>
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<p>Some examples of polynomials in one variable are: 3x + 7, 5x2 + 6x - 7, 6x2 + 9x + 3x3. </p>
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<p>Some examples of polynomials in one variable are: 3x + 7, 5x2 + 6x - 7, 6x2 + 9x + 3x3. </p>
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<h3>3.What is the degree of a polynomial?</h3>
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<h3>3.What is the degree of a polynomial?</h3>
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<p>The degree of a polynomial is the highest exponent of its variable. For example, in 5x3 + 8x2 + 6x, the degree of the polynomial is 3 as 3 is the highest value of the exponent. </p>
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<p>The degree of a polynomial is the highest exponent of its variable. For example, in 5x3 + 8x2 + 6x, the degree of the polynomial is 3 as 3 is the highest value of the exponent. </p>
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<h3>4.What are the types of polynomials based on degree?</h3>
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<h3>4.What are the types of polynomials based on degree?</h3>
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<p>Zero or constant, linear, and quadratic polynomials are different<a>types of polynomials</a>based on their degree. </p>
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<p>Zero or constant, linear, and quadratic polynomials are different<a>types of polynomials</a>based on their degree. </p>
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<h3>5.Is 5 a constant polynomial?</h3>
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<h3>5.Is 5 a constant polynomial?</h3>
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<p>Yes, 5 is a constant polynomial, because it can be written in the form 5x0. </p>
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<p>Yes, 5 is a constant polynomial, because it can be written in the form 5x0. </p>
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<h3>6.What should parents know about polynomials in one variable to help their child?</h3>
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<h3>6.What should parents know about polynomials in one variable to help their child?</h3>
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<p>Parents should know that a polynomial in one variable is an expression with only one variable (like x), raised to different powers.</p>
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<p>Parents should know that a polynomial in one variable is an expression with only one variable (like x), raised to different powers.</p>
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<h3>7.How can parents make learning polynomials interesting for their child?</h3>
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<h3>7.How can parents make learning polynomials interesting for their child?</h3>
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<p>Parents can use real-life examples for instance,<a>comparing</a>each term in a polynomial to items in a store. Only similar items (like terms) can be added together.</p>
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<p>Parents can use real-life examples for instance,<a>comparing</a>each term in a polynomial to items in a store. Only similar items (like terms) can be added together.</p>
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<h3>8.How can parents explain the “degree” of a polynomial to their child?</h3>
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<h3>8.How can parents explain the “degree” of a polynomial to their child?</h3>
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<p>Parents can tell their child that the degree is simply the highest power of the variable. For example, in , the degree is 3 because x3 has the highest exponent.</p>
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<p>Parents can tell their child that the degree is simply the highest power of the variable. For example, in , the degree is 3 because x3 has the highest exponent.</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>