Question

Create a unique example of dividing a polynomial by a monomial and provide the simplified form. Explain, in complete sentences, the two ways used to simplify this expression and how you would check your quotient for accuracy.

Answer 1

@DebbieG

Answer 2

can you help? @DebbieG

Answer 3

(x³- 2x² + x – 1) : ( x- 2)= the quotient 3x² +4x+ 9 and reminder 17
Here is the method for calculation
3x² +4x+ 9
------------------------ **
x-2 / 3x³- 2x² + x – 1 \ first 3x³ divide by x the result is 3x²
**** 3x³ - 6x²*********** 3x² multiply by ( x-2)
------------------- * - ******substraction
*******4x² + x **********divide again by x etc +4x
*******4x² -8x ********** 4x multiply by x-2
--------------------* -*******substraction ....etc
*********+9x - 1
*********+9x -18
-----------------------* -
************+17 ***** here is the rest because 17 can’t be divided by x

you can do the same way for

x²+x-2 / 2x⁵-0x⁴+ 3x³- 2x² + x – 1 \

Answer 4

did that help

Answer 5

is it correct? @issrabi

Answer 6

i hope lol

Answer 7

lolol

Answer 8

my math can be a bit wrong maybe but i think it is bro

Answer 9

idk its just all in there its kinda confusing lol sorry :/

Answer 10

its ok sorry if i couldnt help

Answer 11

it did probably...im just to stupid to read it and get it lol.. dnt have a math brain lol

Answer 12

me neither i dont like math but im good at it so u know i have to do it

Answer 13

@DebbieG

Answer 14

Well, first off, @issrabi's polynomial long division example above is a bit confusing... at first I think it was wrong, but it's just that the problem he DID is different than the problem that he STATED.

He stated (x³- 2x² + x – 1)/( x- 2)= the quotient 3x² +4x+ 9 and reminder 17
But he meant to say (3x³- 2x² + x – 1)/( x- 2)= the quotient 3x² +4x+ 9 and reminder 17

As first stated, of course, you get a diffferent result... but in any case, I would not do either by long division, I would use synthetic division (sooooo much easier)....

... but that's neither here not there, since that has nothing do with your problem:

\(\Large \text{Create a unique example of dividing a polynomial}\)
\(\Large \color{red}{ \text{ by a monomial}} \text{ and provide the simplified form.}\)

x - 2 is not a monomial, it is a binomial.

A monomial is a one-term polynomial, and every monomial IS a polynomial (but not every polynomial is a monomial). A polynomial is just a sum of terms that have coefficients and non-negative integer exponents (which can include a constant term).

so:
\(x^4+3x^2+5x-4\) is a polynomial (with 4 terms)
\(3x^2+5x-4\) is a polynomial (with 3 terms, called a trinomial)
\(3x^2-1\) is a polynomial (with 2 terms, called a binomial)
\(5x^6\) is a monomial, which is simply a polynomial with 1 term

So, I suppose, your question is asking you to do something like:

\[\Large \dfrac{ 4x^4+6x^3-8x^2+4x }{ 2x }\]

That is "dividing a polynomial by a monomial ".... But I'm honestly not sure what it is getting at when it says " the two ways used to simplify this expression"??

I guess you might say that one way it to factor the GCF from the numerator and cancel, and another way is to break it up into a sum of individual terms, and then reduce each term?? Eg:

\[\Large \dfrac{ 4x^4+6x^3-8x^2+4x }{ 2x }= \dfrac{ 4x^4}{ 2x }+ \dfrac{ 6x^3}{ 2x }- \dfrac{ 8x^2 }{ 2x }+ \dfrac{4x }{ 2x }\]
????....... not sure.

Answer 15

what you did is correct by the looks it kinda looks like the example in the book

Answer 16

@DebbieG

Answer 17

just confused on what i would put