Question

factor the trinomial completely 7x^3+14x^2+7x+14

Answer 1

This is how I do it. First common factor of 7.

=7(x^3+2x^2+x+2)
=7(x^2+____)(x+______)

Because I know that it has to give x^3, so it has to be x^2 * x. Now I just fill in the blanks. How many x^2 do we have? 2.

=7(x^2+____)(x+2)

How many x's do we have? 1.

=7(x^2+1)(x+2)

1*2=2, so that works!