Question

$x^2 + 11x + 24$
which of the following is equivalent to the given expression?
choose 1 answer:
a $(x + 2)(x + 12)$
b $(x + 3)(x + 8)$
c $(x + 4)(x + 6)$
d $(x + 5)(x + 6)$

Explanation:

Step1: Recall factoring trinomials

To factor \(x^2 + bx + c\), we find two numbers that multiply to \(c\) and add to \(b\). Here, \(b = 11\) and \(c = 24\).

Step2: Find two numbers for 24 and 11

We need two numbers \(m\) and \(n\) such that \(m\times n=24\) and \(m + n = 11\). Checking pairs: \(3\times8 = 24\) and \(3 + 8=11\).

Step3: Factor the trinomial

So, \(x^2+11x + 24=(x + 3)(x + 8)\).

Answer:

B. \((x + 3)(x + 8)\)