How do you factor 6a^2+2a-1-8a^2+56a2+2a−1−8a2+5?

1 Answer
Dylan D.
Jun 22, 2016

-2((a-2)(a+1))−2((a−2)(a+1))

Explanation:

Group like terms
=-2a^2+2a+4=−2a2+2a+4
Factor out the common term (-2)
=-2(a^2-a-2)=−2(a2−a−2)
Now factor in form x^2+bx+cx2+bx+c into (x+a)(x+b)(x+a)(x+b)
Think what numbers add to -1 and multiply to -2
-2 and 1 fit.
Therefore, =-2((a-2)(a+1))=−2((a−2)(a+1))

Let's verify our solution using a=5a=5

-2((5-2)(5+1))=6(5)^2+2(5)-1-8(5)^2+5−2((5−2)(5+1))=6(5)2+2(5)−1−8(5)2+5
-2((3)(6))=6(25)+10-1-8(25)+5−2((3)(6))=6(25)+10−1−8(25)+5
-2(18)=150+10-1-200+5−2(18)=150+10−1−200+5
-36=-50+14−36=−50+14
-36=-36−36=−36

Try for any other aa and it will work.

See https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/factoring-quadratic-expressions-core-algebra/v/factoring-polynomials-1

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