Question

factoring polynomials. [MEDAL. Thanks in advance :3]

Answer 1

\[9a ^{2}+6a-35\]

Answer 2

There's this method my teacher taught me...like the "MAGIC X" ;A; I dunno how to do it.

Answer 3

"magic x" I'm not sure of lol... but you can either factor it...or you can use the quadratic equation which would you like?

Answer 4

XD Lol. Well, I'm supposed to factor each polynomial.

Answer 5

okay...we lets see...we need to find the factors of 35 first...what are the factors of 35?
meaning...what times what...= 35?

Answer 6

Um. -_-" 7*5, 35*1,

Answer 7

that would be correct...don't put the face lol you got it :P

so now...what are the factors of 9?

Answer 8

meaning what times what = 9?

Answer 9

Okay, 3*3, 9'*1

Answer 10

okay...now we check them

we have

(3x - 5)(3x + 7)

check by foiling it out

9x² + 21x - 15x - 35
9x² + 6x - 35

just guess and check using THAT method :)

Answer 11

Oh, okay. That makes sense xD

Answer 12

haha...would you like to know another method that i learned from someone else on here?

Answer 13

Sure. That would be great :D

Answer 14

alright...so first...you know what polynomial form is correct? Ax² + Bx + C

Answer 15

in case not...look at your equation...look a lot like it doesn't it?

Answer 16

Yeess... Sorry for the late reply, I was doing laundry. -_-"

Answer 17

haha not a problem :)

okay

so you multiply your A times your C

what do you get?

Answer 18

I get 315a^2

Answer 19

...sorry should have clarified....you multiply JUST A ...not Ax²....so multiply just the 9 times -35 which is

Answer 20

oh okay.

Answer 21

-315

Answer 22

correct.....now find the factors of THAT number....that add to 6 :)

Answer 23

to save you some time for now lol...the factors are 21 and -15

Answer 24

so now.....

take your Ax (not Ax²) and do this

(Ax + factor 1)(Ax + factor 2) all over A

so in your case it would be

(9x + 21)(9x-15) all over 9

Answer 25

uhuh...

Answer 26

Can I ask, why it would be two 9as?
Because, it's 9a^2. so wouldn't it be 3a? ;/

Answer 27

no you ignore the ² for this method....you'll see why in the next step

Answer 28

okayokay...

Answer 29

what can factor out of each of these parenthesis?

both 9 and 21 are divisable by 3 right?
both 9 and -15 are divisable by 3 right?

so

3(3x + 7) 3(3x - 5) all over 9

now multiply the 3's on top

9 (3x+7)(3x-5) all over 9

what is 9 / 9? they cancel out soooo

we have

(3x + 7)(3x-5)

Answer 30

lol a bit unorthodox and you probably wont use it much...but it's another way to think about it...as factoring gets harder..this makes it A LOT easier

Answer 31

ohkay ohkay ohkay xD

Answer 32

Thanks so much.

Answer 33

haha yeah no problem :)