Synthetic Substitution Worksheet
Practice synthetic substitution for evaluating polynomials and finding roots at a Grade 12 level.
Includes
Standards
Synthetic Substitution Practice
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Follow the instructions for each section. Show all your work for full credit.
Use synthetic substitution to evaluate the polynomial for the given value.
1. f(x) = 2x³ - 5x² + 4x - 10; x = 3
2. g(x) = x⁴ + 3x³ - 7x - 5; x = -2
Use synthetic substitution to determine if the given value is a root (zero) of the polynomial. If it is, write the corresponding factor.
3. Is x = 1 a root of P(x) = 3x³ - 2x² - 5x + 4? If so, the factor is .
4. Is x = -3 a root of Q(x) = x⁴ + 5x³ + 2x² - 8x - 12? If so, the factor is .
5. According to the Remainder Theorem, what is the remainder when P(x) = x³ - 6x² + 11x - 6 is divided by (x - 2)?
-2
0
2
6
Given one root, use synthetic substitution to find the remaining roots of the polynomial.
6. If x = -1 is a root of P(x) = x³ + 4x² + x - 6, find the other roots.