You are not logged in.
Pages: 1
Had a easy math test, but couldn't get the bonus.
Factor Completely: X^6-9X^4-X^2+9
Offline
Offline
Why did the vector cross the road?
It wanted to be normal.
Offline
Looks like I didn't go far enough. Thanks Mathsyperson. But why did you break down the (x^4 - 1) the way you did?
Offline
Oops, looks like I didn't go far enough either. I should have seen that double-difference of squares thing. Ah well. We make a good team.
Why did the vector cross the road?
It wanted to be normal.
Offline
When given a problem on a test, you can use a little trick to cheat, sort of. It also happens to be useful when factoring polynomials over integers mod n.
Simply do the following:
Take P(x) (your polynomial) and plug in 1. If P(1) = 0, then you can take (x-1) out of your polynomial. Try P(2), P(3), P(-1), etc.
But remember, you can really only use this trick because teachers give nice numbers.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
Offline
And another - the degrees of x are only even. So you can plug y=x^2 and the degree of the equation will become form 6 to 3, which is some helpful simplification.
IPBLE: Increasing Performance By Lowering Expectations.
Offline
Pages: 1