Synthetic Substitution Practice Worksheet
Practice problems for synthetic substitution of polynomials, including evaluating functions and determining factors.
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Synthetic Substitution Practice
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Use synthetic substitution to solve the following problems. Show all your work.
1. Use synthetic substitution to evaluate P(x) = 2x³ - 5x² + 4x - 1 for x = 3.
2. Evaluate f(x) = x⁴ + 6x³ - 2x + 7 for x = -2 using synthetic substitution.
3. True or False: If P(2) = 0 for a polynomial P(x), then (x - 2) is a factor of P(x).
True
False
4. True or False: If (x + 1) is a factor of Q(x), then Q(1) must equal 0.
True
False
5. Use synthetic substitution to determine if (x - 4) is a factor of P(x) = x³ - 7x² + 14x - 8. The remainder is .
6. Is (x + 3) a factor of f(x) = 2x³ + 5x² - 4x - 3? The value of f(-3) is .
7. Given P(x) = x³ - kx² + 2x - 4. If P(2) = 0, find the value of k.
8. For what value of 'a' is (x - 1) a factor of x⁴ + ax³ - 3x² + 2x - 5?