Factoring Homework Help?

Question

How do you factor polynomials with four terms, like this.
x^2y^2 - y^2-15x^2 + 15
Where do you start and what do you do?

Answer 1

First you group the 'like terms'; in your example, the first two and the last two. Then you see the common factor and pull it out

y^2(x^2-1) - 15 (x^2-1)
Now you see the common term in both and pull that out
(x^2-1) (y^2-15)

thus you have your two factors of the polynomial

Answer 2

x^2y^2-y^2-15x^2+15
=y^2(x^2-1)-15(x^2-1)
=(y^2-15)(x^2-1)
=(y^2-15)(x-1)(x+1)

I don't know of any general technique to solve.Just solve a lot of questions.Crack your head over them.More you practice,more it becomes part of your instinct.Things will start happening on their own.Hope you understand.

Allahuakbar
Slave of Allah

Answer 3

x^2y^2 - y^2-15x^2 + 15

Y^2(X^2-1)-15(X^2-1)=0
(Y^2-15)(X^2-1)=0
SO Y^2=15
AND X^2=1
X=+1 OR-1
AND Y=SQRT(15)

Answer 4

profchan is right, but you can take it a step or two farther if you want.

(x^2-1) (y^2-15) factors into
(x + 1)(x - 1)(y + √15)(y - √15)