Question

question 8 of 10
find the factorization of the polynomial below.
81x^{2}+72x + 16
a. (9x + 8)(9x + 8)
b. (9x + 4)(9x - 4)
c. (9x + 4)(9x + 4)
d. (9x + 8)(9x - 8)

Explanation:

Step1: Recall perfect - square trinomial formula

A perfect - square trinomial is of the form \(a^{2}+2ab + b^{2}=(a + b)^{2}\). For the polynomial \(81x^{2}+72x + 16\), we have \(a^{2}=81x^{2}\), so \(a = 9x\) (since \((9x)^{2}=81x^{2}\)), and \(b^{2}=16\), so \(b = 4\) (since \(4^{2}=16\)). Also, \(2ab=2\times9x\times4=72x\).

Step2: Factor the polynomial

Using the perfect - square trinomial formula \(a^{2}+2ab + b^{2}=(a + b)^{2}\), substituting \(a = 9x\) and \(b = 4\) into the formula, we get \(81x^{2}+72x + 16=(9x + 4)^{2}=(9x + 4)(9x + 4)\).

Answer:

C. \((9x + 4)(9x + 4)\)