Question

factor the trinomial, if possible. (a - 7b)^2 - 6(a - 7b) + 9 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. (a - 7b)^2 - 6(a - 7b) + 9 = (simplify your answer. factor completely.) b. the polynomial is prime.

Explanation:

Step1: Let \(x = a - 7b\)

Substitute \(x\) into the trinomial, we get \(x^{2}-6x + 9\).

Step2: Factor the quadratic trinomial

We know that \(x^{2}-6x + 9=(x - 3)^{2}\) since \((m - n)^2=m^{2}-2mn + n^{2}\), here \(m=x\), \(n = 3\) and \(x^{2}-6x + 9=x^{2}-2\times3\times x+3^{2}\).

Step3: Substitute \(x=a - 7b\) back

We have \((a - 7b-3)^{2}\).

Answer:

A. \((a - 7b)^{2}-6(a - 7b)+9=(a - 7b - 3)^{2}\)