Answer:
[tex] 2w^2(w + 2)(4w - 3) [/tex]
Step-by-step explanation:
[tex] 8w^4 + 10w^3 − 12w^2 = [/tex]
First, factor out the GCF of all terms, 2w^2:
[tex] = 2w^2(4w^2 + 5w - 6) [/tex]
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
[tex] = 2w^2(4w^2 + 8w - 3w - 6) [/tex]
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.
[tex] = 2w^2[4w(w + 2) - 3(w + 2)] [/tex]
[tex] = 2w^2(w + 2)(4w - 3) [/tex]
