Which binomial expressions are factors of 5x3+8x2−7x−6? select each correct answer. x−1 x + 2 x−2 x + 1

 The correct options are

(A) (x-1)

(B) (x+2).

Step-by-step explanation:  We are given to select the correct binomial expressions that are the factors of the following cubic polynomial :

Factor Theorem :  (x - a) is a factor of the polynomial f(x), if f(a) = 0.

Option (A) :  The given binomial expression is (x-1).

We have

So, (x-1) is a factor of p(x).

Option (B) :  The given binomial expression is (x+2).

We have

So, (x+2) is a factor of p(x).

Option (C) :  The given binomial expression is (x-2).

We have

So, (x-2) is NOT a factor of p(x).

Option (D) :  The given binomial expression is (x+1).

We have

So, (x-1) is NOT a factor of p(x).

Thus, (x-1) and (x+2) are the factors of the given polynomial.

Options (A) and (B) are CORRECT.