Question

Medal and or a fan

Part A: Divide (10x4y3 + 5x3y2 - 15x2y - 25x2y4) by -5x2y. Show your work, and justify each step.

Part B: How would your answer in Part A be affected if the x2 variable in the denominator was just an x?

Part C: What is the degree and classification of the polynomial you got in Part A?

Answer 1

@robtobey

Answer 2

@zepdrix

Answer 3

:o

Answer 4

what

Answer 5

\[\Large\rm \frac{10x^4y^3+5x^3y^2-15x^2y-25x^2y^4}{-5x^2y}\]So we need to do this division, yah?

Answer 6

yes sir

Answer 7

\[\Large\rm =\frac{10x^4y^3}{-5x^2y}+\frac{5x^3y^2}{-5x^2y}-\frac{15x^2y}{-5x^2y}-\frac{25x^2y^4}{-5x^2y}\]We can separate the terms like this.
And do the division piece by piece.
Should work out ok. :o

Answer 8

Or we can do factoring in the numerator if you're more comfortable with that.

Answer 9

Yah let's do that actually.. that makes more sense. Factoring.

Answer 10

Err no factoring would be simply doing the division anyway... blahhh how you wanna do this? :d

Answer 11

which is easiest

Answer 12

\[\Large\rm =\color{orangered}{\frac{10x^4y^3}{-5x^2y}}+\frac{5x^3y^2}{-5x^2y}-\frac{15x^2y}{-5x^2y}-\frac{25x^2y^4}{-5x^2y}\]What do you get for this first term?
Divide the 10 and -5.
Divide x^4 by x^2. (recall that when you divide terms with similar bases, you `subtract` the expoennts).

Answer 13

-2x^2y

Answer 14

10 divide -5 gives us -2.
x^4 divide x^2 gives us x^(4-2) which is x^2.
y^3 divide y gives us y^(3-1) which is y^2.\[\Large\rm \color{orangered}{-2x^2y^2}\]Mmmm ok very good! :)
Do that same process with the other terms.

Answer 15

\[\Large\rm =\color{orangered}{-2x^2y^2}+\frac{5x^3y^2}{-5x^2y}-\frac{15x^2y}{-5x^2y}-\frac{25x^2y^4}{-5x^2y}\]

Answer 16

-1x^1y

Answer 17

-3xy

-5xy^3

Answer 18

In the last two terms keep in mind that we're subtracting these negative values, so it will change them to positive, yes?
\[\Large\rm =-2x^2y^2-xy-\frac{15x^2y}{-5x^2y}-\frac{25x^2y^4}{-5x^2y}\]

Answer 19

\[\Large\rm \frac{x^2}{x^2}\ne x\]

Answer 20

ok so

-3

-5y^3

Answer 21

\[\Large\rm =-2x^2y^2-xy-(-3)-(-5y^3)\]Mmm ok good.
Which simplifies a little bit.

Answer 22

By combining like terms?

Answer 23

No. No like-terms here.
Just combine the negatives.

Answer 24

ok so its xy^4

Answer 25

I that correct @zepdrix

Answer 26

What..?
I don't understand what you did...

Answer 27

I combined the negatives

Answer 28

There are no like-terms.
You shouldn't be combining anything.
Just simplify the negative signs.

Example: \(\Large\rm -(-4)=+4\)

Answer 29

ok so

-2x^2y^2 -xy + 3 + 5y^3

Answer 30

Yes.

Answer 31

o ok so is it the same thing with part B

Answer 32

For part B,
If we had divided by x instead of x^2, we would be dividing by `one less power of x`.
So each term would end up with `one more power of x`.

Answer 33

o ok I see thank you so much man

Answer 34

btw I hope you have a good Shabbat my Jewish brother