Mathematics: What is the area of the composite shape? 18 mi 6 mi mi? 20 mi Next →

What is the area of the composite shape? 18 mi 6

CassidgTab

08.05.2022

(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 :

f(x)=x^3+2x^2-16x-32.

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

We will be using the following factorization formula :

a^2-b^2=(a+b)(a-b).

We have

$f(x)\\\\=x^3+2x^2-16x-32\\\\=x^2(x+2)-16(x+2)\\\\=(x+2)(x^2-16)\\\\=(x+2)(x^2-4^2)\\\\=(x+2)(x+4)(x-4).$

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.

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