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

1 Answer
Jun 22, 2016

-2((a-2)(a+1))

Explanation:

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

Let's verify our solution using a=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(18)=150+10-1-200+5
-36=-50+14
-36=-36

Try for any other a and it will work.

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