How do you factor 6a2+2a18a2+5?

1 Answer
Jun 22, 2016

2((a2)(a+1))

Explanation:

Group like terms
=2a2+2a+4
Factor out the common term (-2)
=2(a2a2)
Now factor in form x2+bx+c into (x+a)(x+b)
Think what numbers add to -1 and multiply to -2
-2 and 1 fit.
Therefore, =2((a2)(a+1))

Let's verify our solution using a=5

2((52)(5+1))=6(5)2+2(5)18(5)2+5
2((3)(6))=6(25)+1018(25)+5
2(18)=150+101200+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