Question

multiply x^2+8x+15/x-4 times x^2-16/2x+6

Answer 1

ahh i like this one >:))

let us factor each one first

x^2 + 8x + 5 ->

x- 4 ->

x^2 - 16 ->

2x + 6 ->

can you factor those?

Answer 2

does x^2 and x have factors? i know that sounds dumb but i just want to make sure..

Answer 3

yep.. i.e x^2 + x = x(x + 1)

Answer 4

but where are you going to use that?

Answer 5

I dont thik I need to use it

Answer 6

ahh yes you wont hehe...so how will you factor the 4 stated expressions?

Answer 7

I might need some help with that

Answer 8

let's start with 2x + 6 since it's the easiest...do you see any factors?

Answer 9

2

Answer 10

good! so if you factor out 2..what will you get?

Answer 11

uhm.. 1?

Answer 12

this is how you'll now

\(\LARGE 2(\frac{2x}{2} + \frac{6}[2}\)

you divide each term by 2

Answer 13

\(2(\frac{2x}{2} + \frac{6}{2})\)

Answer 14

there we go...so what's 2x/2? and 6/2?

Answer 15

x and3

Answer 16

so (2x+6) = 2(x+3) got it?

Answer 17

yeah

Answer 18

let's move on to the next one... \(x^2 - 16\)

Hint: \(\large (a+b)(a-b) = a^2 - b^2 \leftarrow \text{difference of two squares}\)

Answer 19

im not sure

Answer 20

okay...in x^2 - 16 what is your "a^2"?

Answer 21

im sorry im still not sure

Answer 22

hmm you understand that x^2 - 16 is in the form of a^2 - b^2 right?

Answer 23

i didnt know that

Answer 24

wll x^2 - 16 is in that form...you want to change it to (a+b)(a-b) but to do that you need to find a and b...following?

Answer 25

yes got it

Answer 26

so since x^2 - 16 is in that form we assume that a^2 = x^2 and b^2 = 16 got it? because a^2 is in the left of the minus sign, so is x^2. b^2 is in the right of the minus sign, so is 16. got it?

Answer 27

yesh

Answer 28

so we know a^2 = x^2

to find a we square root both sides..what's the answer?

Answer 29

sqare root 16 right?

Answer 30

that's for b...but for a it's square root of x^2...you can simplify sqrt x^2 further..what is it?

Answer 31

it would just be x right?

Answer 32

right! then b= sqrt 16...what is it simplified further?

Answer 33

4

Answer 34

so a = x and b = 4

what is (a+b)(a-b) now?

Answer 35

(x+4)(x-4)

Answer 36

you got it! so let's move on to the next one...the next one is x - 4 can you simplify that further?

Answer 37

i dont think so

Answer 38

right! so we're down to our last one... x^2 + 8x + 3 do you have any ideas how to factor this out?

Answer 39

oh wait..that's x^2 + 8x + 15 pardon the typo

Answer 40

so x, 2 and 5?

Answer 41

uhmm howd you get that?

Answer 42

yeah i dont hink i did that right

Answer 43

well i'll link you to one of my tutorials you may get an idea from there

http://openstudy.com/users/lgbasallote#/updates/4f9bd87ee4b000ae9ed11143

Answer 44

okay

Answer 45

wow dude -___- i just did 44 minutes trying to teach that :/

Answer 46

Thanks for showing me and helping me :)

Answer 47

@ igbasallote

Answer 48

that's the last step anyway..the next steps was what he showed.. and it's @lgbasallote lowercase L

Answer 49

@Mikieangelo this may help