Question

Which binomial expressions are factors of 5x3+8x2−7x−6?

Answer 1

Answer:  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 :

$p(x)=5x^3+8x^2-7x-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

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

$p(1)=5\times1^3+8\times1^2-7\times1-6=5+8-7-6=0.$

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

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

We have

$p(-2)=5\times(-2)^3+8\times(-2)^2-7\times(-2)-6=-40+32+14-6=0.$

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

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

We have

$p(2)=5\times2^3+8\times2^2-7\times2-6=40+32-14-6=52\neq0.$

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

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

We have

$p(-1)=5\times(-1)^3+8\times(-1)^2-7\times(-1)-6=-5+8+7-6=4\neq0.$

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.

Answer 2

Answer:

$(x-1), (x+2)$

Step-by-step explanation:

When I factor $5x^3+8x^2-7x-6$, I get $\left(x-1\right)\left(x+2\right)\left(5x+3\right)$.

Hope this helps!!