Question

question 10 of 10
what is the factorization of the trinomial below?
$4x^2 + 28x + 48$

a. $4(x + 3)(x + 4)$
b. $(x + 2)(x + 16)$
c. $(x + 3)(x + 4)$
d. $4(x + 2)(x + 4)$

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of \(4x^2\), \(28x\), and \(48\). The GCF is \(4\), so factor it out:
\(4x^2 + 28x + 48 = 4(x^2 + 7x + 12)\)

Step2: Factor the quadratic trinomial

Now factor \(x^2 + 7x + 12\). We need two numbers that multiply to \(12\) and add to \(7\). The numbers \(3\) and \(4\) work:
\(x^2 + 7x + 12 = (x + 3)(x + 4)\)

Step3: Combine the factors

Substitute the factored quadratic back into the expression:
\(4(x^2 + 7x + 12) = 4(x + 3)(x + 4)\)

Answer:

A. \(4(x + 3)(x + 4)\)