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

Ridiculous.

Answer 2

We will say you are given the expression x^2+15x+56 and you are asked to find the other factor when the first factor you received is x+8 .

long division x+8 into x^2+15x+56 always use the leading coefficient of what you want to go into something such as x+8 into X^2+15x+56 how many times does x go into x^2
- x^2+8x
-------------------- since you are dividing you would subtract to get your answer x^2-x^2=0 15x-(+8x) 7x + 56
is equal to 7x how many times does x go into 7x x+7
-7x+56= -7x-56
7x+56
-7x-56
-----------
0

or you could set it up like a fraction which is really what division really is

x^2+15x+56 if the polynomial factors here you can use this method
---------------------
x+8

x^2+15x+56 (x+8) (x+7) what multiplied comes out to 56 and added will equal 15 8,7

(x+8)(x+7)
----------------
(x+8) the 2 x+8 's cancel and you have x+7 as your answer

Answer 3

(3x^3 - 6x^2 + x) / 3x^2
3x^3/3x^2 - 6x^2 / 3x^2 + x/ 3x^2
x^1 - 2x^0 + 1/x^1
x - 2 +1/3x

You divide the first term 3x^3 by 3x^2 and 3 divided by 3 gives you 1 and dividing exponents you subtract so 3 - 2 gives you the x^1 which is actually just x

The second term is -6x^2 divided by 3x^2 and -6 divided by 3 is -2 and x^2 - x^2 is 0 and x^0 will give you one so -2 times 1 will be -2

The third term is x divided by 3x^2
so 1 - 2 is -1 so the x is on the bottom (denominator) with the 3 and you need a 1 on the top (numerator) 1/3x

so if I take x-2 + 1/3x and I multiply by 3x^2 I get 3x^3 - 2x^2 + 3x^2/ 3x which simplifies to x
which is what we started out with.

Answer 4

Let's our polynomial be
\[x^2+3x+3\]
For simplicity I've taken a quadratic:)

Answer 5

Okay.

Answer 6

Sorry it's \[x^2+3x+2\]

Answer 7

Alright.

Answer 8

Let the monomial be
\[x+1\]

Answer 9

Long....

Answer 10

We have to divide the two
\[\frac{x^2+3x+2}{x+1}\]
Let's first simplify this by long division

\(x\)
_________________________________
\(x+1\) | \(x^2+3x+2\)
-(\(x^2+x\))
\(x+2\)


Next step
\(x+2\)
_________________________________
\(x+1\) | \(x^2+3x+2\)
-(\(x^2+x\))
\(2x+2\)
-( \(2x+2\) )
___________________________
0
So we get
\[\large \frac{x^2+3x+2}{x+1}=x+2\]

Answer 11

@careless850 did you understand till here?

Answer 12

It looks all deformed at the top..

Answer 13

Confusing.

Answer 14

@ash2326

Answer 15

I can barely read it. O.O

Answer 16

Sorry, do you understand this