Question

ok...this is the last one i need help with.
(4x4 − 4x2 − 3) ÷ (2x2 − 3)

Answer 1

I think you can factor the numerator..

Answer 2

how would i do that? im taking math online so its hard to get the hang of certain things

Answer 3

Do you know how to factor quadratic trinomials? Even though the numerator is 4th degree it has a quadratic form.

Answer 4

no..not at all :/

Answer 5

ive never been good at factoring

Answer 6

\[4x^4 − 4x^2 − 3=4t^2-4t-3,\:t=x^2\]
Ah, factoring is a critical skill in algebra; so much depends on it.

Answer 7

Do you know how to FOIL multiply two binomials?

Answer 8

first,outer,inner,last right?

Answer 9

Right. Factoring a quadratic trinomial is just the reverse of that process.

Answer 10

oh crap..

Answer 11

:-D
It's not too bad.
The first step is to split the middle term, so you see what the inner and outer terms were before they were combined. You do that by multiplying the leading coefficient (4) by the constant (-3). Then find factors of that number that add to make the middle coefficient.

Answer 12

im not gonna lie....i still dont understand. i get what youre telling me...but my brain doesnt wanna do it

Answer 13

OK, baby steps: what is 4 times -3?

Answer 14

lol. youre the best. -12

Answer 15

Now find two other factors of -12 that you can add together to make -4.

Answer 16

2 and -6 ?

Answer 17

Right, now you can split the middle term, -4x into 2x -6x. Those are the inner and outer products that you get from FOILing.

Answer 18

\[\rightarrow 4x^4+2x^2-6x^2-3.\]
Sorry, I should have said -4t into 2t -6t. Since I did that substitution, but whatever it's all the same.

Answer 19

its ok!

Answer 20

Now that you have four terms, you can factor by grouping. i.e.
\[\rightarrow (4x^4+2x^2)+(−6x^2−3)\]
and you can factor those two sets of parentheses separately.

Answer 21

Try that and let me know what you get.

Answer 22

ok
give me a few

Answer 23

ok so.... 2x^2(x^2) + 3 (-2x^2 -1) ? i think im way off but i tried

Answer 24

Close.. When you divide 4x^4+2x^2 by 2x^2, you should get (2x^2+1).
For the second set of parentheses, you can factor out that -1.

Answer 25

oh...so is it 2x^2(x^2) +(2x^2+1) ?

Answer 26

Just a couple details missing there:
2x^2(x^2+1) +3(2x^2+1)

Answer 27

You can always check your factoring by multiplying back what you got and see if it matches what you started with.

Answer 28

Oops, I missed something too:
2x^2(2x^2+1) +3(2x^2+1)

Answer 29

youre so awesome for sticking with me for an hour haha

Answer 30

There it is. Now at this step, you'll see that the quantities in parentheses are the same, so you can factor those out and be left with\[(2x^2+1) (2x^2+3)\]

Answer 31

Heh, don't have much else to. :"> I'm waiting for my girlfriend to get off work, so we can go out to dinner.

Answer 32

Though now I'm thinking that it would have been quicker to show you polynomial long division.

Answer 33

awwwww!! hahahaha

Answer 34

Oops again. Dang I keep getting distracted and making silly mistakes, it's (2x^2-3) not 2x^2+3. The -1 was factored out.

Answer 35

But anyway, you see now that you have common factors in the fraction that cancel leaving you with just 2x^2+1, right?