Question

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

Answer 1

`-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