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.

• 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.