Question

I did the long division but how do I explain if 3x+1 is the factor of the dividend ?

Answer 1

can you ellaborate a little?

Answer 2

the remiander will be zero

also, if it IS a factor

P(x) = (3x+1) Q(x) + R(x)

when 3x+1 = 0 ...., x=-1/3

P(-1/3) = (0) Q(-1/3) + R(-1/3)

P(-1/3) = R(-1/3)

if P(-1/3) = 0, then (3x+1) is a factor

Answer 3

I posted a picture

Answer 4

Can you see it ?

Answer 5

did you attach a file? or a link?

Answer 6

attached a file i did it form my phone

Answer 7

no post with pick is present on my end

Answer 8

same here

Answer 9

regardless

is the dividend equal to 0 when x=-1/3 ?

Answer 10

okay let me posted it form the computer one sec i just really need help and i dont get it

Answer 11

It doesn't have to equal zero, Though I need to see the whole problem to understand your question

Answer 12

of course it has to equal zero ...

P(x) factors into A(x) Q(x)

let A(x) = (3x+1)

P(x) = (3x+1) Q(x), when 3x+1 = 0, P(x) = 0

Answer 13

if P(-1/3) is not equal to 0, then (3x+1) is not a factor

Answer 14

not in polynomial division

Answer 15

im talking of polynomial division ....

Answer 16

dividend is just what you are dividing by. Something can be a factor of the dividend and not =0

Answer 17

is 3x+1 not a factor of (9x^2-1)?

Answer 18

but, I think we need to see the question, I think her question is how to express the remainder

Answer 19

dividend
------- = quotient
divisor

Answer 20

can you see it ?

Answer 21

i just attached a file

Answer 22

(3x+1) is a factor of the dividend, the top ... when 3x+1 = 0

Answer 23

ok, so you are trying to answer the second part yea? So the only way a number or polynomial is a factor of another, is if you can divide them and be left with a remainder of zero.

Answer 24

so i have to divide the answer with 3x+1
?

Answer 25

You cannot need decimals with numbers, and with polynomials, you cannot have any left over

Answer 26

no, you are just looking at your answer

Answer 27

so you divided by 3x+1 right? Did you have a remainder?

Answer 28

3

Answer 29

\[\frac{P(x)}{3x+1}=Q(x)\]
\[P(x)=(3x+1)~Q(x)~:~definition ~of~factors\]
\[P(-1/3)=(3(-1/3)+1)~Q(-1/3)\]
\[P(-1/3)=(-1+1)~Q(-1/3)\]
\[P(-1/3)=(0)~Q(-1/3)\]
\[P(-1/3)=0\]

Answer 30

so, the rule in order for something to be a factor is that there is no remainder ie remainder=0. So, can 3x+1 be a factor if you have remainder 3?

Answer 31

no it cannot be a factor because i have a remainder of 3

Answer 32

Then you have answered your question.

Answer 33

my answer is 3x+1 is not a factor of the dividend because in order for something to be a factor im supposed to have a remainder of 0 but i have a remainder of 3 that is why 3x+1 is not a factor

Answer 34

is that correct ? just wanted to double check

Answer 35

that's a good answer. Do you understand why you must have a remainder of zero though?

Answer 36

umm ..i just know its the rule .. thats what you told me lol

Answer 37

ok, so let's go with why that is the rule. It plays off of what amistre's saying.

Answer 38

sa, if you listed the factors of 8 you'd have, 1,2,4,8 right?

Answer 39

okay
:)

Answer 40

if I divide 8 by any of those numbers, will I get a whole number?

Answer 41

umm no?

Answer 42

really? what is 8 divided by 2?

Answer 43

wait

Answer 44

:D lol

Answer 45

i just got it yes you get a whole number

Answer 46

ok, so ie you have no remainder

Answer 47

8*2=16

Answer 48

8/2=4

Answer 49

oh i thought you said multiply sorry :S

Answer 50

so factor just means that when you divide the big number by a factor, you always get a whole number

Answer 51

oh okay:)

Answer 52

so does it make sense now?

Answer 53

yeah :D thank you very much !!!!!!