Polynomial Division Worksheet
Grade 12 math worksheet on dividing polynomials using synthetic and long division, including questions with remainders and missing terms.
Includes
Standards
Polynomial Division
Name:
Date:
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Read each question carefully and show all your work. Use synthetic division where appropriate, otherwise use long division.
1. Divide (x³ + 2x² - 5x + 12) by (x - 2).
2. Perform synthetic division to find the quotient and remainder of (2x⁴ - 3x² + 5x - 1) ÷ (x + 1).
3. Use long division to divide (3x³ - 4x² + 7x - 5) by (x² + x - 1).
4. Find the quotient and remainder when (x⁴ - 2x³ + 5x² - 8x + 4) is divided by (x - 3).
5. When dividing a polynomial P(x) by (x - c), if the remainder is 0, then (x - c) is a of P(x).
6. Synthetic division can only be used when the divisor is a linear factor of the form .
7. What is the remainder when (x⁵ - 3x⁴ + 2x² - 7) is divided by (x - 1)?
-7
-5
0
1
8. If (x + 2) is a factor of P(x) = x³ + kx² - 4x + 12, find the value of k.
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