Question

The step by step solve problem

Help me understand step by step how to divide this following monstrosity? will fan and medal!
@phi
(8x^4y^3 + 4x^3y^2 - 2x^2y - 12x^2y^4) divided by -2x^2y

Answer 1

first, did you know when you subtract fractions like
\[ \frac{10}{20} - \frac{5}{20} \]
you have the same denominator so you do this
\[ \frac{10}{20} - \frac{5}{20}= \frac{10-5}{20} \]
?

Answer 2

yes, but is this not some sort of polynomial division or something?

Answer 3

poly means many (in Greek I think)
you have only one term, so it's not very poly.. (its a monomial ... mono means 1)
though you could call it a polynomial... most people would not bother)

Answer 4

I am just curious as to the step by step on how to solve this thing xD I learn best from visual references and text

Answer 5

the point is that the fraction idea works the other way:
\[ \frac{10-5}{20}=\frac{10}{20} - \frac{5}{20} \]
and that idea works for your problem.
in other words, notice your denominator you have a -2

that means (if it divides evenly) you should divide -2 into each term up top.
to get a "new top"
can you do that?

Answer 6

so divide each term above by -2? like 8x^4y^3/-2 and so on?

Answer 7

yes. we are doing this in small steps

Answer 8

what did you get?

Answer 9

-4x^4y^3?

Answer 10

notice that
\[ \frac{8 x^4 y^3}{-2}= \frac{8}{-2} x^4 y^3 \]

Answer 11

yes 8 divided by -2 is -4
so you get -4 * x^4 * y^3
for the first term.

but you also have to divide -2 into all the terms in the top.

Answer 12

so 4x^3y^2/-2 would be -2x^3y^2?

Answer 13

and we are dividing each by not -2 but the whole denominator?

Answer 14

after you get the new top
you now have
\[ \frac{-4x^4y^3 -2x^3y^2+x^2y + 6x^2y^4}{x^2y}\]

Answer 15

now you can divide each term by y
remember that , for example y^3 means y*y*y
so when you divide y*y*y by y
you get
\[ \frac{y}{y} \cdot y \cdot y\]
which is 1*y*y or \(y^2\)
most people do it the"fast way" and do "top exponent" minus bottom exponent
in other words y^3 / y^1 simplifies to y^2

Answer 16

so then that changes -4x^4y^3 into -4x^4y^2?

Answer 17

yes. now do the other 3 terms that are up top

Answer 18

y^2/y^1 should be y correct? and then y^4/y^1=y^3?

Answer 19

@phi what next?

Answer 20

ok. what do you have for the top now ?

Answer 21

-4x^4y^2 - 2x^3y - x^2y + 6x^2y^3

Answer 22

the third term is not correct. first, it should be positive, because you did -2/-2 and that is +1
then you should have done y/y and that is 1

Answer 23

so it would be cancelled out?

Answer 24

\[ \frac{-4x^4y^2 -2x^3y^1+x^2y^0 + 6x^2y^3}{x^2} \]
I make the y's exponent in the third term y^(1-1) = y^0
anything to the zero power is 1

(which is another way to do y/y = 1). anyway, yes it "cancels",

Answer 25

now divide x*x into each term up top.
the fast way: top exponent minus 2 (2 is the bottom x's exponent)
the simple way: if you have x*x*x*x and you divide by x*x
two of the x's are cancelled. either way, you get x*x or x^2 up top in the first term

Answer 26

-4x^2y^2 - 2x3y + x2y + 6xy^3?

Answer 27

what did you do?
so far we have
\[ \frac{-4x^4y^2 -2x^3y^1+x^2 + 6x^2y^3}{x^2} \]
remember the x^2 is divided into each term up top

Answer 28

o lol 1sec

Answer 29

confused now xD the last term didn't come up right so far I have -4x^2y^2 - 2xy + y + 6xy^3

Answer 30

the 3rd term was originally
- 2x^2y
and you divide that by the original -2x^2 y
notice you do *not* get y

Answer 31

the fourth (last) term is
\[ \frac{6x^2y^3}{x^2} \]

if you have x*x up top divided by x*x below, you get x/x * x/x or 1*1 or 1
i.e. the x^2 is "cancelled" by the x^2 down below

Answer 32

so itd be 6y^3?

Answer 33

for the 4th term, yes
what do you get for the third term?

Answer 34

didn't we make the 3rd term a positive tho?

Answer 35

yes, it will be positive.

Answer 36

so I have to solve x^2y/x^2?

Answer 37

not exactly. re-do that one from scratch:
\[ \frac{-2 x^2 y}{-2 x^2 y} \]

Answer 38

-1?

Answer 39

-2/-2 is not -1

Answer 40

minus divided by minus is plus

Answer 41

1

Answer 42

yes. so the answer is
\[ -4x^2y^2 -2xy+1 + 6y^3 \]

Answer 43

though I might write it in this order
\[ 6y^3 -4x^2y^2 -2xy+1\]

Answer 44

what kind of polynomial is it?

Answer 45

find the "highest degree" term by adding up the exponents of the variables in each term

Answer 46

4th degree polynomial?

Answer 47

for example, 6y^3 has just 3 as the exponent
-4x^2 y^2 has 2+2 = 4
-2xy has 1+1 (x^1 * y^1) so 2
and +1 has no variables so 0

the highest degree term is 4

so it's a 4th degree polynomial

Answer 48

Thanks!