Question

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

Explanation:

Step1: Recall perfect square trinomial formula

The perfect square trinomial formula is \(a^{2}+2ab + b^{2}=(a + b)^{2}=(a + b)(a + b)\).

Step2: Identify \(a\) and \(b\) in the given expression

For the expression \(4x^{2}+28x + 49\), we can rewrite \(4x^{2}\) as \((2x)^{2}\) and \(49\) as \(7^{2}\). Now, check the middle term: \(2ab=2\times(2x)\times7 = 28x\), which matches the middle term of the given expression.

So, comparing with \(a^{2}+2ab + b^{2}\), we have \(a = 2x\) and \(b=7\).

Step3: Factor the expression

Using the perfect square trinomial formula, \(4x^{2}+28x + 49=(2x + 7)^{2}=(2x + 7)(2x + 7)\)

Answer:

\((2x + 7)(2x + 7)\) (corresponding to the option " \((2x + 7)(2x + 7)\)")