Question

thanks for the help earlier I got one more question

X^4-13X^2+36
How do I factor this using algebra not just gussing and checking this times this and what number plus what number gives you these numbers

how do i factor that wihtout playing one of those games were you like guess and check your like taught in nineth grade thanks

Answer 1

part of the "game" that I play is to realize that both brackets have to start with x^2 to have x^4 at the front and x^2's in the middle, so ...

(x^2 - ...)(x^2 - ...)

looking at the +36 at the end, I know my 2 numbers must both have the same sign, since I see a negative in the middle, they must be negative.
Now what two factors of 36 have a sum of 13
Gee, my game tells me it must be 9 and 4
so
(x^2 - 9)(x^2 - 4)
at this point you have to recognize the difference of square for both of those.
final result:
(x+3)(x-3)x+2)x-2)

thanks for playing.