Synthetic Substitution Worksheet

Synthetic Substitution Practice

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)?

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.