MATH SOLVE

4 months ago

Q:
# Factor the polynomial completely.Find a GCF: –2x2 + 2 + 5x3 – 5x GCF = –2 GCF = 5xFactor 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)

Accepted Solution

A:

Answer:Option D is correctStep-by-step explanation:The original polynomial is: –2x2 + 2 + 5x3 – 5xArranging 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.