g(x)=x^2-8x-20

Question

factor step-by-step

Answer 1

To factor the quadratic function g(x) = x^2 - 8x - 20, we need to find two numbers that multiply to -20 and add up to -8 (the coefficient of the x term).

The two numbers that meet those criteria are -10 and 2, because (-10)(2) = -20 and (-10) + 2 = -8.

Now, we can rewrite the quadratic function as:

g(x) = x^2 - 10x + 2x - 20

Grouping the terms, we get:

g(x) = x(x - 10) + 2(x - 10)

Factoring out the common factor (x - 10), we get:

g(x) = (x + 2)(x - 10)

Therefore, the factored form of the quadratic function g(x) = x^2 - 8x - 20 is:

g(x) = (x + 2)(x - 10)