Question

Is it possible to factor `y=6x^2+48x-54`? If so, what are the factors?

Answer 1

Yes; `x=9 and x=-1`

Explanation:

Factoring `Ax^2+Bx+C`
Find factors of `AC` that add up to `B`

Original equation:
`y=6x^2+48x-54`

Simplify by factoring out `6`:
#y=6(x^2+8-9)

Multiply `A` by `C`:
`1•(-9)`
`-9`
x
Find factors of `-9`
`1, -9`
`9,-1`
`3,-3`

Determine which of the factors add up to `B.` Here, `B=8`.

The two factors that add up to `8` are `9,-1`.

Now, you can plug the factors back into the equation.
`y=6(x+9)(x-1)`

Or you can set the factors equal to zero and solve for `x`
You should end up with `x=1` and `x=-9`.