which is the completely factored form of 4x² + 28x + 49?\n(x + 7)(4x + 7)\n4(x + 7)(x + 7)\n(2x + 7)(2x +…

Explanation:

Step1: Recall perfect - square trinomial formula

The perfect - square trinomial formula is (a^{2}+2ab + b^{2}=(a + b)^{2}). For the quadratic expression (4x^{2}+28x + 49), we can rewrite (4x^{2}=(2x)^{2}), (49 = 7^{2}), and (28x=2\times(2x)\times7).

Step2: Factor the quadratic expression

Using the perfect - square trinomial formula (a^{2}+2ab + b^{2}=(a + b)^{2}), where (a = 2x) and (b = 7), we get (4x^{2}+28x + 49=(2x + 7)^{2}=(2x + 7)(2x + 7)).

Answer:

C. ((2x + 7)(2x + 7))