Question

Use the Factor Theorem to determine whether x+2 is a factor of P(x) = x^4 + x^3 - 2x - 12Specifically, evaluate P at the proper value, and then determine whether x + 2 is a factor.p(? ) =?O1. x + 2 is a factor of P(x)O2.x + 2 is not a factor of P (x)

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

P(x) = x^4 + x^3 - 2x - 12

factor = x + 2

Step 02:

Factor Theorem

P(a) = 0

x + 2

P(-2) = 0

`P(-2)=(-2)^4+(-2)^3-2(-2)-12`

P(-2) = 16 - 8 + 4 - 12

P(-2) = 0

The answer is:

P(-2) = 0

x + 2 is a factor of P(x)