Question

8 w 4 + 10 w 3 − 12 w 2 Factor completely

Answer 1

`2w^2(w + 2)(4w - 3)`

Explanation:

`8w^4 + 10w^3 − 12w^2 =`

First, factor out the GCF of all terms, 2w^2:

`= 2w^2(4w^2 + 5w - 6)`

Now we work on the trinomial.

Think of ax^2 + bx + c.

Multiply ac

ac = 4 * (-6) = -24

Now we need two numbers whose product is -24 and whose sum is 5.

They are -3 and 8.

We break up the middle term, 5w, into a sum using these two numbers.

5w = 8x - 3w

`= 2w^2(4w^2 + 8w - 3w - 6)`

Now we factor by parts. We factor a common factor out of the first two terms, and we factor a common factor out of the last two terms.

`= 2w^2[4w(w + 2) - 3(w + 2)]`

`= 2w^2(w + 2)(4w - 3)`