Question

Factor the polynomial completely.

Find a GCF: –2x2 + 2 + 5x3 – 5x
GCF = –2 GCF = 5x
Factor out the GCF: –2(x2 – 1) + 5x(x2 – 1)

Which product of prime polynomials is equivalent to the original polynomial?

(–2 – 5x)(x2 – 1)
(–2 + 5x)(x2 – 1)
(–2 – 5x)(x – 1)(x + 1)
(–2 + 5x)(x – 1)(x + 1)

Answer 1

Answer: the answer is D

Explanation:

the screen has proof it is correct... also please STOP deleting my answers its all ways the same person and its getting really annoying when im giving you the correct answer, im just trying to help :(

Answer 2

Option D is correct

Explanation:

The original polynomial is:

–2x2 + 2 + 5x3 – 5x

Arranging in decreasing power of x:

`5x^3 - 2x^2 -5x+2`

Factoring the given polynomial by grouping:

`5x^3 - 2x^2 -5x+2\\=5x^3-5x- 2x^2+2\\=5x(x^2-1)-2(x^2-1)\\=(5x-2)(x^2-1)`

Now, (x^2-1) can be further solved using formula:

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

Solving:

`=(5x-2)(x^2-1)\\=(5x-2)(x-1)(x+1)`

So,
`(5x-2)(x-1)(x+1)` represents the factors of
`-2x2 + 2 + 5x3-5x`

Hence Option D is correct.