Question

which is the completely factored form of $4x^2 + 28x + 49$?
○ $(x + 7)(4x + 7)$
○ $4(x + 7)(x + 7)$
○ $(2x + 7)(2x + 7)$
○ $2(x + 7)(x + 7)$

Explanation:

Step1: Recall perfect square trinomial

A perfect square trinomial has the form \(a^2 + 2ab + b^2=(a + b)^2\). For \(4x^{2}+28x + 49\), we can rewrite \(4x^{2}=(2x)^{2}\) and \(49 = 7^{2}\).

Step2: Check the middle term

The middle term should be \(2ab\). Here, \(a = 2x\) and \(b=7\), so \(2ab=2\times(2x)\times7 = 28x\), which matches the middle term of the given trinomial.

Step3: Factor the trinomial

So \(4x^{2}+28x + 49=(2x + 7)^{2}=(2x + 7)(2x + 7)\).

Answer:

(2x + 7)(2x + 7)