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2026-01-01
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<p>156 Learners</p>
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<p>188 Learners</p>
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<p>Last updated on<strong>October 28, 2025</strong></p>
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<p>Last updated on<strong>October 28, 2025</strong></p>
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<p>Polynomials are expressions consisting of variables, constants, and exponents. Based on their degrees, polynomials are classified into different types. In this article, we will learn about the three main types of polynomials.</p>
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<p>Polynomials are expressions consisting of variables, constants, and exponents. Based on their degrees, polynomials are classified into different types. In this article, we will learn about the three main types of polynomials.</p>
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<h2>What are Linear, Quadratic, and Cubic Polynomials?</h2>
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<h2>What are Linear, Quadratic, and Cubic Polynomials?</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>▶</p>
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<p>Linear, quadratic, and cubic are the three main<a>types of polynomials</a>. We shall learn more about them in the following sections. </p>
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<p>Linear, quadratic, and cubic are the three main<a>types of polynomials</a>. We shall learn more about them in the following sections. </p>
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<h2>What are Linear Polynomials?</h2>
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<h2>What are Linear Polynomials?</h2>
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<p>A<a>polynomial</a>with a degree of one is known as a<a></a><a>linear polynomial</a>. Here, the highest<a>exponent</a>of the<a>expression</a>is one. It is of the form p(x) = ax + b, where a ≠ 0. Examples of linear polynomials are:</p>
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<p>A<a>polynomial</a>with a degree of one is known as a<a></a><a>linear polynomial</a>. Here, the highest<a>exponent</a>of the<a>expression</a>is one. It is of the form p(x) = ax + b, where a ≠ 0. Examples of linear polynomials are:</p>
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<p>p(x) = 3x + 2. </p>
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<p>p(x) = 3x + 2. </p>
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<p>q(x) = 𝜋y + 5</p>
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<p>q(x) = 𝜋y + 5</p>
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<p>r(z) = -8z</p>
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<p>r(z) = -8z</p>
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<h2>What are Quadratic Polynomials?</h2>
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<h2>What are Quadratic Polynomials?</h2>
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<p>A polynomial where the highest<a>exponent</a>is 2 is known as a<a>quadratic polynomial</a>. The quadratic polynomial will be in the form of p(x) = ax2 + bx + c, where a ≠ 0. Examples of quadratic polynomials are:</p>
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<p>A polynomial where the highest<a>exponent</a>is 2 is known as a<a>quadratic polynomial</a>. The quadratic polynomial will be in the form of p(x) = ax2 + bx + c, where a ≠ 0. Examples of quadratic polynomials are:</p>
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<p>p(x) = 5x2 + 2x + 2</p>
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<p>p(x) = 5x2 + 2x + 2</p>
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<p>q(y) = y2 - 2</p>
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<p>q(y) = y2 - 2</p>
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<p>s(z) = 7z2 + z</p>
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<p>s(z) = 7z2 + z</p>
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<h2>What are Cubic Polynomials?</h2>
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<h2>What are Cubic Polynomials?</h2>
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<p>In a<a>cubic polynomial</a>, the highest exponent of the<a>variable</a>is 3. Its general form is p(x) = ax3 + bx2 + cx + d, where a ≠ 0. Here are a few examples of cubic polynomials: </p>
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<p>In a<a>cubic polynomial</a>, the highest exponent of the<a>variable</a>is 3. Its general form is p(x) = ax3 + bx2 + cx + d, where a ≠ 0. Here are a few examples of cubic polynomials: </p>
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<ul><li>p(x) = x3 + 4x2 - 3x + 2 </li>
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<ul><li>p(x) = x3 + 4x2 - 3x + 2 </li>
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<li>q(x) = 2x3 - 6 </li>
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<li>q(x) = 2x3 - 6 </li>
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<li>r(x) = x3 + 2x</li>
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<li>r(x) = x3 + 2x</li>
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</ul><h2>Tips and Tricks to Master Linear, Quadratic and Cubic Polynomials</h2>
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</ul><h2>Tips and Tricks to Master Linear, Quadratic and Cubic Polynomials</h2>
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<p>Mastering polynomials becomes easier with the right tips and tricks. These techniques help you solve equations faster, avoid common mistakes, and understand concepts better. With consistent practice and smart strategies, you can handle linear, quadratic, and cubic problems confidently.</p>
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<p>Mastering polynomials becomes easier with the right tips and tricks. These techniques help you solve equations faster, avoid common mistakes, and understand concepts better. With consistent practice and smart strategies, you can handle linear, quadratic, and cubic problems confidently.</p>
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<ul><li><p>Identify the degree first it tells you how many roots or turning points the polynomial has. Linear is degree 1, quadratic is 2, and cubic is 3. </p>
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<ul><li><p>Identify the degree first it tells you how many roots or turning points the polynomial has. Linear is degree 1, quadratic is 2, and cubic is 3. </p>
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</li>
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<li><p>Write down<a>coefficients</a>clearly before solving. It keeps your substitution and calculations error-free. </p>
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<li><p>Write down<a>coefficients</a>clearly before solving. It keeps your substitution and calculations error-free. </p>
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</li>
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<li><p>Visualize the graph to understand behavior. Linear gives a line, quadratic a parabola, and cubic an S-curve. </p>
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<li><p>Visualize the graph to understand behavior. Linear gives a line, quadratic a parabola, and cubic an S-curve. </p>
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</li>
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</li>
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<li><p>Always try to factorize before applying<a>formulas</a>. It’s quicker and gives more insight into how the roots form. </p>
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<li><p>Always try to factorize before applying<a>formulas</a>. It’s quicker and gives more insight into how the roots form. </p>
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</li>
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<li><p>Set the polynomial equal to zero to find its roots. That’s the golden rule for solving any<a>polynomial equation</a>.</p>
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<li><p>Set the polynomial equal to zero to find its roots. That’s the golden rule for solving any<a>polynomial equation</a>.</p>
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</li>
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</li>
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</ul><h2>Common Mistakes and How to Avoid Them in Linear, Quadratic, and Cubic Polynomials</h2>
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</ul><h2>Common Mistakes and How to Avoid Them in Linear, Quadratic, and Cubic Polynomials</h2>
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<p>When learning about polynomials, especially linear, quadratic, and cubic types, it is normal to make mistakes. That’s why it’s important to learn about a few common mistakes beforehand, so that we can avoid them in the future.</p>
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<p>When learning about polynomials, especially linear, quadratic, and cubic types, it is normal to make mistakes. That’s why it’s important to learn about a few common mistakes beforehand, so that we can avoid them in the future.</p>
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<h2>Real Life Applications of Linear, Quadratic, and Cubic Polynomial</h2>
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<h2>Real Life Applications of Linear, Quadratic, and Cubic Polynomial</h2>
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<p>Polynomials are widely used in real-life situations. From calculating how much something costs to predicting how a ball moves, here are some of the examples of the real-life applications of linear, quadratic, and cubic polynomials.</p>
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<p>Polynomials are widely used in real-life situations. From calculating how much something costs to predicting how a ball moves, here are some of the examples of the real-life applications of linear, quadratic, and cubic polynomials.</p>
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<ul><li><strong>Mathematics & Algebra:</strong>Linear polynomials are used in<a>solving equations</a>, such as calculating cost or solving word problems. Quadratic polynomials are used to solve problems like finding the area of a rectangle when only the relationship between the length and the width is known. Also, cubic polynomials can appear when finding how much water a box-shaped tank can hold, especially if the dimensions depend on a variable.</li>
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<ul><li><strong>Mathematics & Algebra:</strong>Linear polynomials are used in<a>solving equations</a>, such as calculating cost or solving word problems. Quadratic polynomials are used to solve problems like finding the area of a rectangle when only the relationship between the length and the width is known. Also, cubic polynomials can appear when finding how much water a box-shaped tank can hold, especially if the dimensions depend on a variable.</li>
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</ul><ul><li><strong>Engineering & Construction:</strong>In engineering and construction, linear polynomials are used to estimate materials,<a>quadratic equations</a>are used in designing curved structures like arches and bridges, and cubic polynomials help design complex shapes like road curves and ramps.</li>
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</ul><ul><li><strong>Engineering & Construction:</strong>In engineering and construction, linear polynomials are used to estimate materials,<a>quadratic equations</a>are used in designing curved structures like arches and bridges, and cubic polynomials help design complex shapes like road curves and ramps.</li>
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</ul><ul><li><strong>Technology & Computer Graphics:</strong>Linear polynomials can be used to create simple animations. For example, quadratic polynomials are used to draw smooth curves, and cubic polynomials create realistic 3D movements.</li>
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</ul><ul><li><strong>Technology & Computer Graphics:</strong>Linear polynomials can be used to create simple animations. For example, quadratic polynomials are used to draw smooth curves, and cubic polynomials create realistic 3D movements.</li>
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<li><strong>Physics & Motion: </strong>Polynomials describe motion, velocity, and acceleration. Quadratic and cubic equations help model the path of moving objects like projectiles or cars.</li>
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<li><strong>Physics & Motion: </strong>Polynomials describe motion, velocity, and acceleration. Quadratic and cubic equations help model the path of moving objects like projectiles or cars.</li>
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</ul><ul><li><strong>Economics & Business</strong>: Economists use polynomials to predict<a>profit</a>, cost, and revenue trends. For example, quadratic models show maximum profit points or minimum cost levels.</li>
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</ul><ul><li><strong>Economics & Business</strong>: Economists use polynomials to predict<a>profit</a>, cost, and revenue trends. For example, quadratic models show maximum profit points or minimum cost levels.</li>
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</ul><h3>Problem 1</h3>
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</ul><h3>Problem 1</h3>
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<p>Solve the linear equation: 2x + 5 = 11.</p>
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<p>Solve the linear equation: 2x + 5 = 11.</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>To find the value of x, the first step is to subtract 5 on both sides of the equation.</p>
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<p>To find the value of x, the first step is to subtract 5 on both sides of the equation.</p>
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<p>2x + 5 - 5 = 11 - 5</p>
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<p>2x + 5 - 5 = 11 - 5</p>
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<p>Now, the equation becomes:</p>
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<p>Now, the equation becomes:</p>
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<p>2x = 6</p>
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<p>2x = 6</p>
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<p>Divide both sides by 2 to isolate x.</p>
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<p>Divide both sides by 2 to isolate x.</p>
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<p>2x/2 = 6/2</p>
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<p>2x/2 = 6/2</p>
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<p>x = 3</p>
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<p>x = 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>Solve the quadratic equation: x2 - 5x + 6 = 0.</p>
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<p>Solve the quadratic equation: x2 - 5x + 6 = 0.</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 = 2 or x = 3 </p>
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<p>x = 2 or x = 3 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Let’s use the factorization method to solve the quadratic equation:</p>
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<p>Let’s use the factorization method to solve the quadratic equation:</p>
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<p>x2 - 5x + 6 = (x - 2)(x - 3)</p>
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<p>x2 - 5x + 6 = (x - 2)(x - 3)</p>
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<p>Now set each factor to 0.</p>
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<p>Now set each factor to 0.</p>
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<p>x - 2 = 0; x - 3 = 0</p>
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<p>x - 2 = 0; x - 3 = 0</p>
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<p>Therefore, x = 2, x = 3.</p>
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<p>Therefore, x = 2, x = 3.</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>Solve the cubic equation: x3 - 6x2 + 11x - 6 = 0.</p>
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<p>Solve the cubic equation: x3 - 6x2 + 11x - 6 = 0.</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 = 1, 2, 3 </p>
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<p>x = 1, 2, 3 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Factorizing the polynomial, we get:</p>
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<p>Factorizing the polynomial, we get:</p>
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<p>x3 - 6x2 + 11x - 6 = (x - 1)(x - 2)(x - 3)</p>
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<p>x3 - 6x2 + 11x - 6 = (x - 1)(x - 2)(x - 3)</p>
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<p>Setting each factor to 0,</p>
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<p>Setting each factor to 0,</p>
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<p>x - 1 = 0</p>
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<p>x - 1 = 0</p>
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<p>x - 2 = 0</p>
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<p>x - 2 = 0</p>
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<p>x - 3 = 0</p>
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<p>x - 3 = 0</p>
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<p>Therefore, x = 1, 2, and 3.</p>
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<p>Therefore, x = 1, 2, and 3.</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>Solve the quadratic equation: x2 + 7x + 10 = 0</p>
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<p>Solve the quadratic equation: x2 + 7x + 10 = 0</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 = -2 or x = -5 </p>
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<p> x = -2 or x = -5 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Let’s use the factorization method again.</p>
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<p>Let’s use the factorization method again.</p>
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<p>x2 + 7x + 10 = (x + 2)(x + 5)</p>
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<p>x2 + 7x + 10 = (x + 2)(x + 5)</p>
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<p>Setting the equation to 0, we get:</p>
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<p>Setting the equation to 0, we get:</p>
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<p>x + 2 = 0</p>
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<p>x + 2 = 0</p>
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<p>x = -2</p>
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<p>x = -2</p>
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<p>x + 5 = 0</p>
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<p>x + 5 = 0</p>
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<p>x = -5</p>
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<p>x = -5</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>Solve the linear equation: 3x - 9 = 0</p>
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<p>Solve the linear equation: 3x - 9 = 0</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>We should add 9 on both sides of the equation to isolate 3x.</p>
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<p>We should add 9 on both sides of the equation to isolate 3x.</p>
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<p>3x - 9 + 9 = 0 + 9</p>
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<p>3x - 9 + 9 = 0 + 9</p>
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<p>3x = 9</p>
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<p>3x = 9</p>
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<p>Now, divide both sides by 3 to isolate x.</p>
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<p>Now, divide both sides by 3 to isolate x.</p>
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<p>3x/3 = 9/3</p>
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<p>3x/3 = 9/3</p>
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<p>x = 3</p>
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<p>x = 3</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Linear, Quadratic, and Cubic Polynomials</h2>
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<h2>FAQs on Linear, Quadratic, and Cubic Polynomials</h2>
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<h3>1.What does ‘degree’ mean in a polynomial?</h3>
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<h3>1.What does ‘degree’ mean in a polynomial?</h3>
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<p>The highest<a>power</a>of the variable in a polynomial is known as its degree.</p>
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<p>The highest<a>power</a>of the variable in a polynomial is known as its degree.</p>
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<h3>2.How do linear, quadratic, and cubic polynomials look on a graph?</h3>
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<h3>2.How do linear, quadratic, and cubic polynomials look on a graph?</h3>
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<p>In the graph, a linear polynomial looks like a straight line. A quadratic polynomial looks like a U-shaped curve (parabola) and a cubic polynomial often looks like an S-curve. </p>
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<p>In the graph, a linear polynomial looks like a straight line. A quadratic polynomial looks like a U-shaped curve (parabola) and a cubic polynomial often looks like an S-curve. </p>
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<h3>3.How many solutions can a linear, quadratic, and cubic polynomial have?</h3>
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<h3>3.How many solutions can a linear, quadratic, and cubic polynomial have?</h3>
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<p>A linear polynomial can have only one solution, a quadratic polynomial can have up to two solutions, and a cubic polynomial can have up to three real solutions.</p>
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<p>A linear polynomial can have only one solution, a quadratic polynomial can have up to two solutions, and a cubic polynomial can have up to three real solutions.</p>
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<h3>4.What is a coefficient in a polynomial?</h3>
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<h3>4.What is a coefficient in a polynomial?</h3>
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<p>A<a>coefficient</a>in a polynomial refers to the numerical value that precedes a variable. For example, in the equation 2x + 5, 2 is the coefficient of x. </p>
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<p>A<a>coefficient</a>in a polynomial refers to the numerical value that precedes a variable. For example, in the equation 2x + 5, 2 is the coefficient of x. </p>
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<h3>5.What is a constant?</h3>
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<h3>5.What is a constant?</h3>
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<p>Constant is a<a>number</a>or value that doesn’t change in a polynomial equation. For example, in the equation 2x + 3, 3 is a constant.</p>
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<p>Constant is a<a>number</a>or value that doesn’t change in a polynomial equation. For example, in the equation 2x + 3, 3 is a constant.</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>