Factoring trinomials with a leading coefficient of 1

Question

5W^4-35W^3+50W^2 

Answer 1

First, you wanna factor the greatest common factor of the three monomials making up the trinomial, i.e.

5w^4 - 35w^3 + 50w^2 = 5w^2 (w^2 - 7w + 10)

Now, you can easily further factor the resulting trinomial. If you find the roots w1, w2 of the associated quadratic equation w^2 - 7w + 10 = 0, so that w^2 - 7w + 10 = (w - w1)(w - w2).

either you apply the delta formula, or you remember the notable result that w1+w2 = -7 and w1w2 = 10, from which you can easily get w1 = 2, w2 = 5.

Overall, 5w^4 - 35w^3 + 50w^2 = 5w^2 (w - 2) (w-5)

Answer 2

First factor out Greatest Common Factor, GCF.