Question

How do you factor 2y^2 +5y-18?

Answer 1

`(2y + 9)(y-2)`

Explanation:

We can use the "AC Method" (at least that was the name of the method, which I will explain further, that I was taught) to factor the quadratic equation `2y^2 + 5y - 18`.

Why is it called the "AC Method," you may ask?

In the standard quadratic equation `ax^2 + bx + c = y`, we are going to be first working with the `a` and the `c` coefficients. (Just replace the `x`'s with `y`'s -- variables can be changed for the purposes of understanding the concept pertaining to your question.)

The `a` and the `c` coefficients in the equation you posted are `2` and `-18`, respectively.

So in this method, what we do first is multiply the `a` and the `c` together: `2(-18) = -36`.

Then we find factors that will result in the product of `-36` but when they are added together will result in the sum of the `b` coefficient (which is `5` in this case).

Aha! We have found `-4` and `9` because `-4(9) = -36` and `-4 + 9 = 5`.

Now we expand and write an unsimplified version of the equation.
`2y^2 - 4y + 9y - 18 =0`

Now we factor by grouping...
`2y(y - 2)` and `9(y-2)`

Notice I just paired two terms in the expanded form of the equation and factored through GCF (Greatest Common Factor). Also, notice the sharing of the expression `y-2` (this is extremely important).

Put `2y` and `9` together into `(2y + 9)` and we already have `(y-2)`.

That's it! Our factored equation is `(2y + 9)(y-2)`. Multiply it out and you should hopefully get back to `2y^2 + 5y - 18`.

*I suggest you look for videos for this method because explaining it through written words, speaking from my experience, did not help me fully grasp the concept. *