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

1 Answer
Dylan D.
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

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