Is the binomial a factor of the polynomial function? f(x)=x3+2x2−16x−32

select yes or no for each binomial.

(x−2)

(x+2)

(x−4)

(x+4)

(x+6)

 (A) No, (B) Yes, (C) Yes, (D) Yes, (E) No.

Step-by-step explanation:  We are given to whether each binomial is a factor of the following polynomial or not :

To select the correct factors, we need to factorize the given polynomial.

We will be using the following factorization formula :

We have

Therefore, the factors of the given polynomial are (x + 2), (x + 4) and (x - 4).

Thus,

option (A) : (x - 2)

No.

option (B) : (x + 2)

Yes.

option (C) : (x - 4)

Yes.

option (D) : (x + 4)

Yes.

option (A) : (x + 6)

No.