Synthetic Substitution Practice Worksheet
Practice worksheet for synthetic substitution, suitable for grade 9 algebra students.
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Synthetic Substitution Practice
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Use synthetic substitution to evaluate the following polynomials at the given value. Show all your work.
1. Evaluate P(x) = 2x³ - 5x² + 4x - 10 for x = 3.
2. Find P(-2) for P(x) = x⁴ + 3x³ - 7x - 5.
When using synthetic substitution for P(x) = 3x⁵ - 2x³ + x - 7, the coefficients in order are: 3, 0, , 0, , -7.
For P(x) = x⁶ - 5x⁴ + 2x² - 1, the coefficients are: 1, , -5, , 2, , -1.
3. If P(x) = x³ - 6x² + 11x - 6 and P(1) = 0, which of the following is a factor of P(x)?
(x + 1)
(x - 1)
(x + 6)
(x - 6)
4. What is the remainder when x⁴ - 8x² + 6 is divided by (x - 2)?
2
-10
-6
16
5. If P(c) = 0, then (x - c) is a factor of P(x).
True
False
6. Synthetic substitution can only be used when dividing by a linear factor of the form (x - c).
True
False
7. Given that (x - 4) is a factor of P(x) = x³ - 10x² + 29x - 20, use synthetic substitution to find the other factors.