Question

How would i factor a simple question like 3a^2 + 2

Answer 1

3a^2 and 2 have nothing in common (except 1), so that cannot be factored

Answer 2

i just still dont understand....oh boy..

Answer 3

what about one like 3a^2 + 9?

Answer 4

the GCF of 3 and 2 is 1

there are no variables common between them, which is why the GCF of 3a^2 and 2 is 1

Answer 5

3a^2 and 9 have a 3 in common though

Answer 6

so you can factor out 3 to get

3a^2 + 9 = 3(a^2 + 3)

Answer 7

Oh i see how that one works now. thanks. and for the one i just asked....what does it mean by putting it in factored form?

Answer 8

it just means factor it as much as possible

Answer 9

example: if you factor the number 10, then you would get 2*5

Answer 10

2*5 is the factored form

Answer 11

like how would i factor that one out...?

Answer 12

to factor 3a^2 + 9 completely, you would get

3a^2 + 9 = 3(a^2 + 3)

and that's all you can do

Answer 13

3(a^2 + 3) is the factored form

Answer 14

OHHHHHH, THANK YOU SO MUCH. you are a hero

Answer 15

you're welcome, glad it's making sense now

Answer 16

:D

Answer 17

wait wait...

Answer 18

what if in the directions it said x^2 + 3x + 2

Answer 19

to factor that expression? would that work the same way?

Answer 20

sort of...but you would use a different trick now

Answer 21

the last term is 2

the middle coefficient is 3

Answer 22

you want to find two numbers that multiply to 2 (last term) AND add to 3 (middle coefficient) at the same time

Answer 23

which two numbers do this?

Answer 24

well... 1 x 2 = 2 and 2 + 1 = 3
so.... 2?

Answer 25

i think......

Answer 26

good, so the two numbers are 1 and 2

Answer 27

which means x^2 + 3x + 2 factors to (x + 1)(x + 2)

Answer 28

you can check by expanding (x + 1)(x + 2) out and you'll get x^2 + 3x + 2 back again

Answer 29

oh yay! I see how that works. what if their was a number in front of the x

Answer 30

then it would be slightly different, but you would use the same basic idea

Answer 31

do you have anything in mind?

Answer 32

as in 4n^2 - 20n +25

Answer 33

ok first you would multiply 4 (the first coefficient) and 25 (last term) to get

4*25 = 100

Answer 34

now you must find two numbers that

a) multiply to 100

AND

b) add to -20

at the same time

Answer 35

uhhh

Answer 36

i understand how to do it now but i cant figure out what goes into each

Answer 37

how about -1 and -100

-1 + (-100) = -101

no that doesn't work

Answer 38

-2 and -50 ?

-2 + (-50) = -52

nope, doesn't work either

Answer 39

-4 and -25?

-4 + (-25) = -29

still no

Answer 40

-5 and -20 ?

-5 + (-20) = -25

no, but we're getting closer

Answer 41

-10 and -10?

-10 + (-10) = -20

which works

Answer 42

yeah i see that

Answer 43

so we break up the -20n into -10n-10n to get this

4n^2 - 10n - 10n +25

Answer 44

then you would factor by grouping

Answer 45

like terms?

Answer 46

first group the terms into pairs

4n^2 - 10n - 10n +25

(4n^2 - 10n) + (-10n +25)

Answer 47

then factor each group separately

Answer 48

(4n^2 - 10n) + (-10n +25)

2n(2n - 5) + (-10n +25)

2n(2n - 5) - 5(2n - 5)

see what to do next?

Answer 49

kinda ish

Answer 50

what do you think the next step is

Answer 51

distributing

Answer 52

yes in a way, but in reverse

Answer 53

notice we have the common term of (2n-5)

Answer 54

factoring outt.... i think

Answer 55

so we factor that out to get this

(2n - 5)(2n - 5)

Answer 56

ohhh i see

Answer 57

if we had

x(2n-5) + y(2n-5)

we would factor out the (2n-5) to get

(x+y)(2n-5)

Answer 58

oh i think i get it thank you!!!! gold star for you!

Answer 59

ok glad it's all making sense, you'll be a pro in no time and you'll have to change your user name lol

Answer 60

haha!! i just never grasp the concepts with my teacher!! haha hopefully i can change it though!!

Answer 61

you can definitely change it, just keep practicing and you'll be fine

Answer 62

will do!!!! haha

Answer 63

lol good, and also try to get things in terms of your own language

no sense in repeating the same thing over and over again if you don't know how to translate

Answer 64

thats so true! i dont even know most terms! its crazy! thanks for the advice:)

Answer 65

you're welcome, you might do well to write them on flash cards or something. That usually helps me

Answer 66

yeah ill do that forsure!! and jusst wondering, are you in highschool?

Answer 67

no I'm in college learning to become a teacher

Answer 68

ohhh man! thats really cool! hope you are successful!!

Answer 69

me too, thanks lol

Answer 70

no problem!