Synthetic Substitution Practice Worksheet

Synthetic Substitution Practice

Read each question carefully and use synthetic substitution to solve the problems. Show all your work for full credit.

Use synthetic substitution to evaluate the following polynomial functions at the given value.

1. If P(x) = 3x³ - 2x² + 5x - 7, find P(2).

2. If P(x) = x⁴ + 4x³ - x - 10, find P(-1).

Use synthetic substitution to determine if the given value is a root of the polynomial. If it is, write 'Yes, it is a root.' If not, write 'No, it is not a root.'

3. Is x = 3 a root of P(x) = x³ - 6x² + 11x - 6?  

4. Is x = -2 a root of P(x) = 2x³ + 7x² + 4x - 4?  

5. When the polynomial P(x) = x³ - 4x² + 2x + 5 is divided by (x - 1), what is the remainder?

6. Given that (x - 4) is a factor of P(x) = x³ - 10x² + 31x - 30, use synthetic substitution to find the other factors of the polynomial.

Determine if the following statements are true or false.

7. Synthetic substitution can only be used when dividing by a linear factor of the form (x - k).

8. If P(k) = 0 using synthetic substitution, then k is a root of the polynomial P(x).