Factor the trinomial 10a2 33aw 20w2 Select the correct cho

Factor the trinomial. 10a^2 - 33aw + 20w^2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 10a^2 - 33aw + 20w^2 = (Factor completely.) B. The trinomial is prime.

Solution

Option A

Heres the work

10a^2 - 33aw + 20w^2

This is a quadratic, so we use the middle term split method...

a = 10 , b = -33 and c = 20

We need two numbers that multiply to ac(10*20) =200
and we need two numbers that add to b(-33)

sum = -33
product = 200

Well, -25 and -8 works, right?
Yeah it does!

So, we write tis as :

10a^2 - 25aw - 8aw + 20w^2

Now, we factor each group :
5a(2a - 5w) - 4w(2a - 5w)

And now factor (2a-5w) in common to finally get :

(5a - 4w)(2a - 5w) -----> ANSWER