Okay -- this one factors nicely.
If you're not yet comfortable using the Quadratic Formula, you could try guess-and-check.
I'm going to assume that you already understand why the factorization needs this form:
(y + M)(y + N)
where the product M*N is -2x^2.
So, you could start substituting factors of -2x^2 for symbols M and N, and then multiply out the factorization to see if it works. If it does not work, then try a different pair of factors for -2x^2.
Alternatively, you could multiply out (y + M)(y + N) first:
y^2 + (M+N)*y - M*N
From this we see that M+N must equal x and M*N must equal -2x^2. Now, think back to how you factored quadratic trinomials with A=1 that had numerical coefficients for B and C (instead of symbolic ones, like x and -2x^2). You look for two quantities whose produce is C and whose sum is B, yes?
In other words, find two factors of -2x^2 that add to make x. Those two factors are M and N.
Have you learned Polynomial Long Division? That's another method for guessing one factor (like x+y, for example) and then using division to find the other factor (the check is whether you get a remainder of zero).
If I didn't want to guess and check, I would probably use the Quadratic Formula. It's fairly straightforward, here, because the Discriminant (B^2-4AC) turns out to be a squared expression (i.e., the radical sign goes away).
Treat y as the variable, and treat x as constant. Then:
A = 1
B = x
C = -2x^2
The factorization will take the form (y - r
1)(y - r
2) where r
1 and r
2 are the roots that you get from the Quadratic Formula.
Whichever way you decide to go, please show your work, if you need more help. :cool:
