Use the Factor Theorem to determine whether x 3 is a factor

Use the Factor Theorem to determine whether x + 3 is a factor of P(x) = x^4 + 2x^3 - 2x - 6. Specifically, evaluate P at the proper value, and then determine whether x + 3 is a factor. x + 3 is a factor of P(x) x + 3 is not

Solution

WE have to find if x + 3 is a factor

Here\'s how we do it :
x + 3 = 0
x = -3

Plug that in :

(-3)^4 + 2(-3)^3 - 2(-3) - 6

81 - 54 + 6 - 6

27

So, when we divide, we get a remainder of 27. This is not zero.

So, since f(a) was not zero, (x - a) is not a factor

P(-3) = 27 ---> ANSWER

Thus here (x + 3) is NOT a factor ---> ANSWER