Question

I'm having a problem with algebra. I'm supposed to simplify this problem: 3x^2 + 7x +2 OVER 4x^2-16. Anyone know how to start? I'm trying to break down the top into theFOIL method but having a hard time figuring out what 2 numbers are going to get me a positive 7x and a positive 2.

Answer 1

forget that; i lost my place in reading

Answer 2

3x^2 + 7x +2

first times last

3*2 = ?

Answer 3

6

Answer 4

good; the last sign is + which tells us we add; the middle sign is + which tells
us we add + and +

(x+ ?/3) (x+ ?/3)

what are the factors of 6 that add up to 7?

Answer 5

6 and 1

Answer 6

good, then lets fill; them in

(x+ 6/3) (x+ 1/3)

reduce the fractions

(x+ 2) (x+ 1/3)

if theres still a fraction stick the bottom in front

(x+ 2) (3x+ 1)

and we are done with it

Answer 7

factor the bottom part and cancel out like "terms"

Answer 8

I don't think I can simplify the bottom anymore. It is 4x^2-16. I have it simplified as (2x-4)(2x+4)
So I think my answer would just be (x+2)(3x+1) OVER 2x-4)(2x+4). Id that right?

Answer 9

factor out a 2 from each one

Answer 10

ideally youd factor out a 4 first; but either way you get to it in the end :)

Answer 11

Ok. Totally lost now. Sorry.

Answer 12

can you factor out a 2 from each of your denominator parts?

Answer 13

4x^2 - 16 = 4 (x^2 - 4) = 4 (x-2) (x+2)

or your way

4x^2 - 16 = (2x-4) (2x+4) = 2(x-2) 2(x+2) = 4 (x-2) (x+2)

Answer 14

I see it. So then I could cancel out the x+2 from the top and bototm.

Answer 15

yep

Answer 16

Got it! Even more important, I understand it!! Thank you!