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

1 Answer
Mar 4, 2018

#(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. *