factor completely.\n7 + 14x + 7x² =
factor completely.\n7 + 14x + 7x² =
Answer
Explanation:
Step1: Factor out the GCF
First, find the greatest - common factor (GCF) of the terms (7), (14x), and (7x^{2}). The GCF is (7). So, (7 + 14x+7x^{2}=7(1 + 2x+x^{2})).
Step2: Recognize the perfect - square trinomial
The expression (1 + 2x+x^{2}) is a perfect - square trinomial of the form (a^{2}+2ab + b^{2}=(a + b)^{2}), where (a = 1) and (b=x). So, (1 + 2x+x^{2}=(1 + x)^{2}).
Answer:
(7(1 + x)^{2})