Question

Can somebody help me with this?

Explain why the binomial (x + 2) IS a factor of this polynomial expression.
Explain why the binomial (x + 1) IS NOT a factor of this polynomial expression.

Answer 1

We are given polynomial:
`5x^3+8x^2-7x-6`.

We need to explain why the binomial (x + 2) IS a factor of this polynomial expression and why the binomial (x + 1) IS NOT a factor of this polynomial expression.

Let us set first factor equal to 0 and solve for x.

x+2=0

x=-2.

Plugging x=-2 in given polynomial, we get

`5(-2)^3+8(-2)^2-7(-2)-6 = 5(-8) +8(4)+14-6`

`= -40 +32+14-6`

`=0`

Because x=-2 gives 0 on plugging in given polynomial, so it's factor of given polynomial expression.

Now, let us check second factor x+1=0

x=-1.

Plugging x=-1 in given polynomial, we get

`5(-1)^3+8(-1)^2-7(-1)-6 = 5(-1) +8(1)+7-6`

=-5+8+7-6.

= -4.

Because x=-1 doesn't gives 0 on plugging in given polynomial, so it's not a factor of given polynomial expression.