Quotient of (x³ – 3x² + 3x – 2) ÷ (x² – x + 1)
2026-02-28 23:31 Diff

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Last updated on October 4, 2025

The result we get when we divide one polynomial by another polynomial is called the quotient. The quotient can be another polynomial or a simpler expression, depending on the polynomials involved. We will learn about the quotient of (x³ – 3x² + 3x – 2) ÷ (x² – x + 1) below.

What is the Quotient of (x³ – 3x² + 3x – 2) ÷ (x² – x + 1)?

To find the quotient of (x³ – 3x² + 3x – 2) ÷ (x² – x + 1), we can perform polynomial long division. Here are the steps:

Step 1: Divide the first term of the dividend by the first term of the divisor. So, divide x³ by x² to get x.

Step 2: Multiply the entire divisor (x² – x + 1) by x and subtract the result from the original dividend.

Step 3: The new dividend becomes (–2x² + 3x – 2).

Step 4: Repeat the division by dividing the first term of the new dividend (–2x²) by the first term of the divisor (x²) to get –2.

Step 5: Multiply the entire divisor by –2 and subtract from the current dividend.

Step 6: The remainder is 0, indicating the division is exact. The quotient is x – 2.

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Important Glossaries of Polynomial Division

  • Quotient: The result obtained after dividing one polynomial by another.
  • Polynomial: An algebraic expression consisting of variables and coefficients.
  • Dividend: The polynomial being divided.
  • Divisor: The polynomial by which we divide the dividend.
  • Remainder: The polynomial that remains after division. If it is 0, the division is exact.

Jaskaran Singh Saluja

About the Author

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.

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