Question

sjld

Answer 1

@sarahusher

Answer 2

So for example take
polynomial \[p(x)=4x ^{3}+12x^{3}+8x\]
and let monomial
\[m(x)=4x\]
where a monomial is a polynomial with one term and rational coefficients

if you have
\[\frac{ p(x) }{ m(x) } =\frac{ 4x ^{3}+12x ^{2}+8x }{ 4x } \]

You can prove the quotient in two ways:
1) long division
2) cancellation rule

That is the approach I would take to this question :)

Answer 3

@sarahusher can I use this example as my answer? :/

Answer 4

You can if you want, but I think it would be good practice to come up with one as well so you understand how it works :)

Answer 5

@sarahusher ookay :) thank you so much!!

Answer 6

No problem :) let me know if you come up with another example and I can check it for you!

Answer 7

@sarahusher okay is long division where you take the numerators and divide them all by the denominator? & subtract the exponents? What's the cancellation rule? :0

Answer 8

yes! that is long division

The cancellation rule is just where you try to factorise out common factors so that you get the simplest form :)

Answer 9

okay & how do you do that with that example problem you showed me above? I did the long division but I've never done the cancellation rule before :/ i feel dumb lol @sarahusher

Answer 10

okay, so put the bigger number on top, the little one below
so we get
\[\frac{ 4x ^{3}+12x ^{2}+8x }{ 4x } = \frac{ 4x(x ^{2}+3x+2) }{ 4x(1) }=\frac{ 4x }{ 4x }\times \frac{ x ^{2}+3x+2 }{ 1 }\]
\[= 1\times( x ^{2}+3x+2)=(x+2)*(x+1)\]

Answer 11

and don't feel dumb :)
practice makes perfect!

Answer 12

@sarahusher :) omg you're a lifesaver!! thank youuu!

Answer 13

ha no problem dear, just keep practising :)