Question

question 5 of 10
factor the trinomial below.
$x^2 + 5x - 24$

a. $(x - 4)(x + 6)$
b. $(x - 8)(x + 3)$
c. $(x - 6)(x + 4)$
d. $(x - 3)(x + 8)$

Explanation:

Step1: Recall factoring trinomial form \(x^2 + bx + c\)

We need two numbers that multiply to \(c = -24\) and add up to \(b = 5\).

Step2: Find the two numbers

Let the numbers be \(m\) and \(n\) such that \(m\times n=-24\) and \(m + n = 5\).
By checking factors of \(-24\):

• \(8\times(- 3)=-24\) and \(8+( - 3)=5\).

Step3: Write the factored form

The trinomial \(x^2+5x - 24\) can be factored as \((x - 3)(x + 8)\) since \((x - 3)(x + 8)=x^2+8x-3x - 24=x^2 + 5x-24\).

Answer:

D. \((x - 3)(x + 8)\)