Question

Can anyone give me a clear definition about H.C.F and L.C.M of polynomial?

eg1) Find the H.C.F of \((x-1)(x ^{2}-4x+4)\) and \((x ^{2}-2x)(x ^{2}-1)\) .

eg2) Find the L.C.M. of \(x ^{2}-1\) and \((x+1)^{2}\) .

Answer 1

I'm assuming that is like highest common factor or something?

Answer 2

how about LCM? lowest common mutiply?

Answer 3

I have to assume it is just like finding the LCM of 3 and 4

Answer 4

that's 12, isnt it?

Answer 5

yea,

Answer 6

find factors of x^2-4x + 4 and factors of x^2 -2x and x^2 -1 and then see what is H.C.F.

Answer 7

(x-1)(x^2-4x+4)=(x-1)(x-2)^2

Answer 8

(x^2-2x)(x^2-1)=x(x-2)(x-1)(x+1)

Answer 9

then the HCF is (x-1)(x-2)???

Answer 10

factors of x^2 -4x + 4 = (x-2)(x-2)

Answer 11

you can have it BPD, I've never heard these terms before in my life, I'm using guesswork based off of other situations. I would say the highest common factor is the biggest quantity that divides (x-1)(x-2)^2

Answer 12

factors of x^2 - 2x are (x)(x-2)

Answer 13

so I agree with your answer kryton

Answer 14

factors of x^2 - 1 (difference of two squares) are (x-1)(x+1)

Answer 15

Now if you list your factors (no repeat):
(x)(x-2)(x-1)(x-1)
(x-1)(x-2)(x-2)
the highest common factor in both of these is (x-2)

Answer 16

I disagree there

Answer 17

another way of looking at H.C.F. is something that will divide into both of these

Answer 18

Now that I know for certain it is just like with integers, I would say the gcm is (x-2)(x-1)

Answer 19

Explain please @FibonacciChick666

Answer 20

as that is a factor of both

Answer 21

can you divide the first factorization you gave evenly by (x-1)(x-2)?

Answer 22

yes, you are right @FibonacciChick666, I missed that! yes it's (x-1)(x-2)

Answer 23

\[\frac{(x)\not {(x-2)(x-1)}(x-1)}{\not{(x-1)(x-2)}}\]

Answer 24

oh those were supposed to be slashes... but anyways, yea. I have just never seen HCM. In number theory even we used GCD

Answer 25

greatest common divisor

Answer 26

i agree with @FibonacciChick666

Answer 27

thank you @FibonacciChick666 :) i have cleared the concept!

Answer 28

so @kryton1212, the definition I will give you is that the HCM as you call it is the same as the greatest common divisor, which as the name implies, is the absolute biggest number you can divide a pair of polynomials by and have no remainder.

Answer 29

np

Answer 30

it was a group effort, I'm guessing you have to deal with common core?

Answer 31

yup

Answer 32

I am so sorry. I have to teach the idiocy of it in order for the kids I tutor to pass their class....

Answer 33

i am always confused with polynomials

Answer 34

oh never mind haha

Answer 35

well, they really aren't that bad. There are a lot of things worse. What confuses you most?