Answer:
Option D is correct
Step-by-step explanation:
The original polynomial is:
–2x2 + 2 + 5x3 – 5x
Arranging in decreasing power of x:
[tex]5x^3 - 2x^2 -5x+2[/tex]
Factoring the given polynomial by grouping:
[tex]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)[/tex]
Now, (x^2-1) can be further solved using formula:
(a^2-b^2)=(a-b)(a+b)
Solving:
[tex]=(5x-2)(x^2-1)\\=(5x-2)(x-1)(x+1)[/tex]
So, [tex](5x-2)(x-1)(x+1)[/tex] represents the factors of [tex]-2x2 + 2 + 5x3-5x[/tex]
Hence Option D is correct.
