Question

Select the correct steps for factoring the polynomial 5x^3-40

Answer 1

5 (x-2) (x²+2x+4)

Explanation:

Stating with 5x³ - 40, the want to simplify the x part by extracting the common factor, so

5x³ - 40 = 5(x³-8)

Now to factor x³-8, we can rewrite it in the format x³-2³, right?

And there's a formula to obtain x³-y³, which is the Difference of Cubes formula that goes like this: x³-y³= (x-y)(x²+xy+y²)

So, we apply this formula replacing the y with our value of 2:

x³-2³= (x-2)(x²+2x+2²) = (x-2)(x²+2x+4)

So, overall, we have 5x³ - 40 = 5 (x-2) (x²+2x+4)