SOLUTION: 6x^2+7xy-3y^2-8y+10y+c can be factorized, Q: what is c?

Question 1164354: 6x^2+7xy-3y^2-8y+10y+c can be factorized, Q: what is c?
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

It is almost certain that you have not shown the expressions correctly.

Specifically, you show two linear y terms and no linear x term.

It would seem advantageous to you to check your post before you submit it....

Nevertheless, I will go through this with you, because it is an interesting problem.

I have changed the "-8y" term to "-8x"....

We know the coefficient of the x^2 term is AD=6; we need to find the constant term CF.

Since AD is 6, we can have A and D be either 6 and 1, or 3 and 2. It is more likely that they are 3 and 2; so let's try that and see if we can reach an answer.

Equating coefficients with the given expression, we have

Without going through the details (they aren't hard), the first two equations give us B = -1 and E = 3.

Then, knowing B = -1 and E = 3, the last two equations give us

Again without the details, those two equations give us C = 2 and F = -4.

And that gives us our answer: CF = -8.

The result is easily confirmed by doing the multiplication:

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