Question

Factor the following expression completely. (hint: start by factoring out the GCF and then determine what other type of factoring can be used.)4x^2 + 20x + 16

Answer 1

$4x^2+20x+16$

1. Factoring out the GCF:

$=4(x^2+5x+4)$

2. Rewrite the second term in parentheses as a difference (find two numbers that added equals 5 and multiplied 4):

$=4(x^2+4x+x+4)$

3. Factor by grouping:

$=4(x(x+4)+(x+4))$$=4(x+4)(x+1)$

Then, the given expression factored is:

$4x^2+20x+16=4(x+4)(x+1)$