Factoring polynomial

[lmf0610]

2x²+11x-6=

 

[Lizzie]

Since we know that no common number can be divided out of this equation, we can skip that part. So, what do we do now?

Well, you have to start with the 2x².
You know you have to get this separated into two parts...
(2x +/- ?)(x +/- ?)

This takes care of the 2x² because when you multiply 2x by x, you will get 2x². This is the only way that you can break this part up. Now what do you do next?

you still have 11x-6 .... you kind of have to work with these two number at the same time... First, you have to find two numbers that when multiplied together, make -6, and when added together make 11. So, we can easily start by making a list of what numbers multiply to get -6.

You'll get the following list:
-6 x 1
6 x -1
-2 x 3
2 x -3

Now, which ones add up to get 11? None of them!! Oh no, what now? Well, don't freak out because you are forgeting the 2x² that we used just a bit ago.

We need to fit in one of those sets of numbers into what we got earlier...

Now, since we have this...
(2x +/- ?)(x +/- ?), which numbers can we plug in to make the product come out to be 2x²+11x-6? Let's try this out.

(2x-6)(x+1) = (2x)(x)+(2x)(1)+(-6)(x)+(-6)(1) = 2x²+2x-6x-6 = 2x²-4x-6... That doesn't work.

So, just try the rest and you'll find your answer!

 

[stapel]

Is the first term squared, as you have posted it here, or cubed, as you have posted it elsewhere?

Thank you.

Eliz.

P.S. In future, to post corrections of messages, please "reply" with the corrections, rather than starting another thread on the same exercise. Thank you.