Question

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

Select each correct answer.

x−1

x + 2

x−2

x + 1

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

Following are the calculation to the factor of the binomial expressions:

Given:

$\bold{5x^3+8x^2-7x-6}$

To find:

factor=?

Solution:

$\bold{5x^3+8x^2-7x-6}$

Putting the value "-2,-1, 1, and 2" in the above given binomial expression:

When x=-2

$\to \bold{5(-2)^3+8(-2)^2-7(-2)-6}\\\\\to \bold{5(-8)+8(4)-7(-2)-6}\\\\\to \bold{-40+32+14-6}\\\\\to \bold{-46+46}\\\\\to \bold{0}$

When x=-1

$\to \bold{5(-1)^3+8(-1)^2-7(-1)-6}\\\\\to \bold{5(-1)+8(1)-7(-1)-6}\\\\\to \bold{-5+8+7-6}\\\\\to \bold{-11+15}\\\\\to \bold{4}$

When x=2

$\to \bold{5(2)^3+8(2)^2-7(2)-6}\\\\\to \bold{5(8)+8(4)-7(2)-6}\\\\\to \bold{40+32-14-6}\\\\\to \bold{72-20}\\\\\to \bold{52}$

When x=1

$\to \bold{5(1)^3+8(1)^2-7(1)-6}\\\\\to \bold{5(1)+8(1)-7(1)-6}\\\\\to \bold{5+8-7-6}\\\\\to \bold{13-13}\\\\\to \bold{0}$

Therefore the factor is "(x-1) and (x+2)".

Learn more:

brainly.com/question/11429941