factor 𝑥^2−4𝑥−32

To factor the expression 𝑥^2−4𝑥−32, we need to find two binomials whose product is equal to the expression.

First, we need to find two numbers whose product is equal to -32 and whose sum is equal to -4, the coefficient of the middle term.

The factors of -32 are (1, -32), (-1, 32), (2, -16), (-2, 16), (4, -8), and (-4, 8).

Out of these pairs, the pair whose sum is -4 is (4, -8).

So, we can write 𝑥^2−4𝑥−32 as (𝑥+4)(𝑥−8), where 𝑥+4 and 𝑥−8 are the binomial factors.

Therefore, the factored form of 𝑥^2−4𝑥−32 is (𝑥+4)(𝑥−8).