What is the Quotient of (x³ – 3x² + 5x – 3) ÷ (x – 1)

To find the quotient of (x³ – 3x² + 5x – 3) ÷ (x – 1), we can use polynomial long division. Follow these steps to simplify the division process:

Step 1: Write down the dividend (x³ – 3x² + 5x – 3) and the divisor (x – 1).

Step 2: Divide the first term of the dividend by the first term of the divisor: x³ ÷ x = x².

Step 3: Multiply the entire divisor (x – 1) by x² and subtract the result from the dividend: (x³ – 3x² + 5x – 3) - (x²(x – 1)) = (x³ – 3x² + 5x – 3) - (x³ – x²) = -2x² + 5x – 3.

Step 4: Repeat the process with the new polynomial: -2x² ÷ x = -2x. Multiply and subtract: (-2x² + 5x – 3) - (-2x(x – 1)) = (-2x² + 5x – 3) - (-2x² + 2x) = 3x – 3.

Step 5: Repeat again: 3x ÷ x = 3. Multiply and subtract: (3x – 3) - (3(x – 1)) = (3x – 3) - (3x – 3) = 0. The division is complete, with a quotient of x² – 2x + 3.

• Quotient: The result obtained after dividing one polynomial by another.

• Polynomial: An expression consisting of variables and coefficients, involving terms with non-negative integer exponents.

• Dividend: The polynomial being divided.

• Divisor: The polynomial by which the dividend is divided.

• Long Division: A method used to divide polynomials by writing out the steps of the division process.