Question

Find the quotient and remainder. {x²-3x+5}{x-2}

Answer 1

The quotient is x - 1 and the remainder is 3.

Step-by-step explanation:

To find the quotient and remainder when dividing x² - 3x + 5 by x - 2, we can use polynomial long division.

1. First, divide the leading terms of the polynomials: x² / x = x.
2. Multiply the divisor (x - 2) by the quotient obtained in the previous step (x): x * (x - 2) = x² - 2x.
3. Subtract the product from the original polynomial: (x² - 3x + 5) - (x² - 2x) = -x + 5.
4. Next, bring down the next term of the dividend (-x):
5. Divide the new polynomial (-x + 5) by the divisor (x - 2): (-x + 5) / (x - 2) = -1.
6. Multiply the divisor (x - 2) by the quotient obtained in the previous step (-1): -1 * (x - 2) = -x + 2.
7. Subtract the product from the new polynomial: (-x + 5) - (-x + 2) = 3.

Therefore, the quotient is x - 1 and the remainder is 3.