Question

question 7 of 25
which of the binomials below is a factor of this trinomial?
$16x^2 + 24x + 9$

a. $2x + 3$
b. $2x - 3$
c. $4x - 3$
d. $4x + 3$

Explanation:

Step1: Recall perfect square trinomial formula

The perfect square trinomial formula is \(a^{2}+2ab + b^{2}=(a + b)^{2}\).
For the trinomial \(16x^{2}+24x + 9\), we can rewrite \(16x^{2}\) as \((4x)^{2}\) and \(9\) as \(3^{2}\), and \(24x=2\times(4x)\times3\).

Step2: Factor the trinomial

Using the perfect square trinomial formula, where \(a = 4x\) and \(b=3\), we have:
\(16x^{2}+24x + 9=(4x)^{2}+2\times(4x)\times3+3^{2}=(4x + 3)^{2}\)
So the binomial factor of \(16x^{2}+24x + 9\) is \(4x + 3\).

Answer:

D. \(4x + 3\)