Question

q4-3. which expression is equivalent to $x^2 + 10x + 24$?
$square$ $(x + 4)(x + 6)$
$square$ $(x + 1)(x + 24)$
$square$ $(x + 2)(x + 12)$
$square$ $(x + 3)(x + 8)$
clear all

Explanation:

Step1: Identify trinomial form

We have $x^2 + 10x + 24$, which follows $x^2+bx+c$. We need two numbers that multiply to $c=24$ and add to $b=10$.

Step2: Find factor pairs of 24

List pairs: $(1,24)$ sum to 25; $(2,12)$ sum to 14; $(3,8)$ sum to 11; $(4,6)$ sum to 10.

Step3: Write factored form

Use the pair $(4,6)$ to write as $(x+4)(x+6)$.

Answer:

A. $(x + 4)(x + 6)$