Common Factoring Tutorial

this tutorial is on common factoring common factoring is the simplest form of factoring and it's where you divide out a common number or variable from all

terms in a polom let's look at the example 4X Cub + 6 x^2 if we take the factors of 4X Cub

it's going to look like 2 * 2 * x *

x * X okay so we see 2 * 2 is 4 and x * x *

X would give us our X cubed so 4 x cubed can be written as 2 * 2 * x * x * X and that is its simplest

form if we do the same thing with 6 x^2 we're going to have 2 * 3 so that'll give us our 6 and now

we have X2 so we can get that by multiplying x * X so the simplest form of 6x^2 is 2 * 3 * x * X so now we're

going to look at the common factors what factors are common in both of these so I see we have a two that's

common okay I have a three in this one but I don't have one up here so that's not common and I have a two up here but I don't want to have one down here okay so those

aren't common either I do see that I have 2 X's in each and then this x is left over so the

common factors are we have a two we have an X and we have another x 2 * x * X is

going to give us 2 x x^ 2 so if I was looking for the common factors in 4X cub and

6x^2 the answer would be 2x^2 because 2x^2 is in both of those let's look at just finding the

greatest common factor in each of these binomial and we have some trinomials down here so we have 3x + 3 you want to

figure out which number or term is common in both 3x and 3 so right away if I look at 3x I can

see 3x is made up of a three times an X if I look at the three I can see well that's just made three 3

* 1 okay so if I'm looking for the common factor the only thing common in both of those is three so the greatest common factor in

3x and 3 is three let's look at the next one 2X and 4 I want to see what's common in both of

those well I know 2x is made up of Just 2 * X and

four is made up of 2 * 2 so if I look for what's common in both of those I got a two and then I have an X

and a two so those aren't common so the only thing that's common between them is that two so that is the greatest common

factor looking at the next one I have a 2 * X and then just a two so the greatest common factor is two

there's definitely not an X in both so that's not a common factor looking at the next one 3x + 6 we got a three in this one I know

there's a three hidden in that six somewhere so the greatest common factor is three this one's a little bit trickier

it's a trinomial so we have three things here to look at let's first look at 36

x^2 36x squ is made up of 2 * 2 that's

4 * 3 we're at 12 now * 3 is 36 *

x * X if we look at the 12x well 12x is made up of 2 * 2 that

gives us 4 and three more is going to give us a 12 so 2 * 2 * 3 is 12 and of course then we

have an X the last one last term is six which is made up of 2 * 3 so if I was looking to see what's common in each of these we got a

two and we have a three we don't have any X's common because this term doesn't have an X so we can't include an X in there the greatest common factor then is

2 * 3 which is 6 so the biggest thing that can be taken out of each term is

six looking at this one we have an N here but we don't have an N there so I definitely can't take an N Out what's the highest number that goes into both

four and 10 four goes into itself but it doesn't go into 10 two goes into four and two goes into 10 so the greatest common factor is

two looking at this one what is the highest number that goes into both five and 15 well five goes into five and look

at that five goes into 15 so I know I can take a five out look at this one however look at the variables I got one B here so we can consider that as B to

the one and I have two B's b^ 2 so I have B * B so the first term I have B

second term I have B * B so the highest variable I can take out of there is a b we're going to get this one we have 1

x so we can consider that as X to the^ 1 and we have two of them over here this is x * X so the highest possible factor

I can take out or the greatest common factor is X can't take out a number here because all that's here is one so the greatest common factor would be

one look at the next example if I look at the numbers I have a four and a 12 well four goes into itself and four goes into 12 so four is

the greatest common factor now can I take an a out I have an A here but there's no a here so I can't take any A's out of there the Great common factor

is four let's put this all together once you have the greatest common factor you can divide all terms in the

polom by this expression and write what is left over so for an example 3x^2 + 6 x what is the greatest common factor I

can take out of there let's look at the numbers first I have a three and I have a six three goes into three

does three go into six yes it does so I can definitely take a three out let's look at the

X's I have x^2 so that's x * X there's 2 X's there and we can consider this x ^ 1 so we have 1 x there so the greatest

common factor I can take out is an X so 3x is the greatest common factor of 3x^2 + 6x now we have to write what's

left over if we take 3x out of each term we're going to have 3x^2 / 3x so if we were to write that

3x^2 / 3x okay my threes are going to cancel

out and I have x * x / just X so one of these is going to cancel out and I'm left with an X Plus plus

6X divid 3x well I can see right away my x's are going to cancel out they're gone so now I have 6 ID 3 which we know is

two okay so if I was going to factor 3x^2 + 6x my answer is going to be 3x x + 2 if we look at another example 3x + 3

going to take out the greatest common factor first so what's common in both terms 3x and 3 what goes into both of those that's

three can I take an X out well this one doesn't have an X so I can't take an X out let's see what's left over 3x / 3

going to be left with an x 3 / 3 is just

1 so 3x + 3 if I was going to common factor that it would be 3 x + 1 -2 y + 4 remember I'm going to take the greatest common factor out first so

what is the highest possible number or variable that can go into both of these terms well I can see very clearly that two goes into both of those I can't take

out a y because there is no y on this term so what is left over -2 y / 2 so

let's write this over here -2 y / 2 if I cancel out these twos I'm still left with that negative there so I have

y now I have the term four let's divide that by two and we have two left over 2 a - 6 the greatest common factor is

2 can't take an a out because there's no a value here so what's left over when I divide 2 a by 2 I'm left with

a -6 / pos2 gives us a negative 3 5 x - 15 the greatest common

factor is 5 what am I left with well 5x / 5 is X

-5 / 5 is -3 -4 a + 12 what am I going to take out well what number goes into both of those

I know four goes into itself and four goes into 12 so I'm going to take a four out I'm going to take a negative out here

so that inside my bracket I don't have a

negative so4 a /4 is a 12 / -4 is -3 greatest common factor of 4N and 10 so I need a number that goes into both

of those now I know two goes into both of those but does four four goes into itself but four doesn't go into 10 so

it's definitely two I'm left with an n and -10 / 2 is5 so I'm left for the two in

there 8 x^2 + 5 x Cub + x okay I want to find out what is the greatest common factor I can take out of each term so there's definitely not a number

I can take out of each but how many X's can I take out I have two x's here I have three X's here and I only have

one here so the greatest common factor is just going to be my X and now I have to decide what's left over so I'm going

to divide this first term a x^2 if I divide it by X I'm going to be left with 8 x and if I have 5 x cubed I'm going to

divide it by X so I'm just going to take one of those X's away and I'm left with two

2 and I have x / X gives us 1 there's my solution for this last one I have a cub

+ 12 a 2 - 4 a if I was looking for a number to take out the only possible one would be a one since there's a one in front so instead I'm just going to look

at the variables again how many A's can I take out well I have three here I have two here and just one so the biggest

number I could take out is the one if I take an a out of each term I have a cub / a which leaves us with

two 12 a 2 / a is going to leave us with 12 a and -4 a / by a leaves us with just

-4 and there you have it