Use synthetic division to find p(-2) for p(x) = x⁴ + 9x³ - 9x + 2.

Solution:

Synthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor.

One of the advantages of using this method over the traditional long method is that the synthetic division allows one to calculate without writing variables while performing the polynomial division, which also makes it an easier method in comparison to the long division.

Given, p(x) = x⁴ + 9x³ - 9x + 2

We have to find p(-2) by synthetic division.

Therefore, the value of p(-2) is -36.

Use synthetic division to find p(-2) for p(x) = x⁴ + 9x³ - 9x + 2.

Summary:

Using synthetic division the value of p(-2) for p(x) = x⁴ + 9x³ - 9x + 2 is -36.