Question

Which of the following binomials is a factor of the trinomial below?
x^2-5x-24

Answer 1

(x-8) and (x+3)

Explanation:

To find the binomials of the trinomial, we just need to factor in the trinomial.

First,

x² -5x - 24

Then split it, so the terms add to -5 and multiply to -24

x² +3x -8x - 24

Then factor x in the first part, and -8 in the second part.

x(x+3) - 8(x+3)

Factor again

(x-8)(x+3)

Answer 2

Explanation:

Factorize 24. When we add the factors, we have to get (-5) and we multiply we have to get (-24).

So, the factors are 3 and (-8)

When we add 3 +(-8) = -5 ; we multiply we get (-8)*3 =(-24)

Replace the middle terms with the factors.

x² - 5x - 24 = x² - 8x + 3x - 24

= x(x - 8) + 3(x - 8)

= (x - 8)(x+3)