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 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 \(4x^2+28x + 49\)

For \(4x^2=(2x)^2\), so \(a = 2x\). For \(49 = 7^2\), so \(b = 7\).
Check the middle term: \(2ab=2\times(2x)\times7 = 28x\), which matches the middle term of the given trinomial.
So \(4x^2+28x + 49=(2x + 7)^2=(2x + 7)(2x + 7)\).

Answer:

\((2x + 7)(2x + 7)\) (the third option: \((2x + 7)(2x + 7)\))