Factor 16w^4 + 16w² - 140. Show all work.

Answer 1

16w^4 + 16w^2 -140

First make a substitution a=w^2 so this becomes

16a^2 +16a -140

4(4a^2 +4a -35) The quadratic can be factored by grouping. Find 2 numbers multiply to -70(4 x -35) and add to 4. These are +14 and -10. Rewrite 4a as 14a -10a gives us

(4a^2 +14a) + (-10 a -35) and factor both groups to

2a(2a +7) - 5(2a+7) which gives us (2a+7)(2a-5). Now replace a with w^2 and we have

4(2w^2 +7)(2w^2-5)