Question

x^4-x^2-12

Answer 1

notice how we can rewrite the expression as (x^2)^2-x^2-12
in other words if we take a=x^2 then
a^2-a-12 is the expression we seek to factor.
This one is simply an easy factoring problem that amounts to (a-4)(a+3). However, you aren't done yet. resubstitute a=x^2 to get
(x^2-4)(x^3+3). Do you think this expression is still factorable?

Answer 2

I don't get why we would rewrite it like that ?

Answer 3

Why we would want to or why we can?

Answer 4

Both?

Answer 5

You can start by diving everything by 2.

Answer 6

so a GCF?

Answer 7

yes.

Answer 8

Oh wait no. Nvm.

Answer 9

Why we want to is simple: you were probalby taught how to factor quadratic trinomial expressions, and we are simply rewriting the expression into something more familiar.

Why we can? It is simply algebra. I can write 2^4 as (2^2)^2 (both equal 16), as I can do so with the variable x. The reason I took a=x^2 was to make the expression more simplified. a is merely a dummy variable so I don't have to type x^2 every time. Each time I see x^2 I replace it with an a.

Answer 10

that's confusing for me.

Answer 11

What is confusing for you?

Answer 12

the replacing X^2 with a

Answer 13

I'm a highschool sophomore. let's dumb this down a ton

Answer 14

Ok. Let's not even replace the x^2 with an a then. Just leave it as is.

Take x^4-x^2-12.

Rewrite the expression as (x^2)^2-(x^2)-12.
Well, treat x^2 like a single variable.
Then you can factor the expression as (x^2+4)(x^2-3)

Answer 15

erm.
(x^2-4)(x^2+3)
If you don't believe me multiply it out.

Answer 16

then notice how you can factor (x^2-4) into (x-2)(x+2). This is a simple formula for difference of squares, if you don't know it's jsut one of those "fun facts".

Answer 17

the final factorization is (x-2)(x+2)(x^2+3)
I am sorry for such a short notice, but you haven't responded to what I've said and I have work I must attend to. Good luck. Bump the question and perhaps tag others if you have any further inquiries.

Answer 18

thank you so much!