Question

What is 24x^2y^6 - 16x^6y^2 + 4xy^2 divided by 4xy^2? Can someone please help ?

Answer 1

what is 24x^2y^6 divided by 4xy^2?

Answer 2

6xy^4

Answer 3

Okay, so that's the first term of the quotient. Now we multiply the divisor (4xy^2) by that, and subtract the result from the dividend (24x^2y^6-16x^6y^2+4xy^2). What do you get when you do that?

Answer 4

So I divide 24xy^6 from 24x^2y^6-16x^6y^2+4xy^2 ?

Answer 5

24x^2y^6 - 16x^6y^2 + 4xy^2 - (6xy^4*4xy^2) =
= 24x^2y^6 - 16x^6y^2 + 4xy^2 - 24x^2y^6
= -16x^6y^2 + 4xy^2

right?

Answer 6

Yea

Answer 7

okay, so we're doing long division, just not writing it out. we've done the first step, and the first term of our answer is 6xy^4. now we're left with dividing -16x^6y^2 + 4xy^2 by 4xy^2

what is -16x^6y^2 divided by 4xy^2?

Answer 8

-16x^6y^2
---------- =
4xy^2

Answer 9

-4x^5y

Answer 10

correct. so multiply -4x^5y by 4xy^2, and subtract that result from what we have left of the original dividend, namely -16x^6y^2 + 4xy^2

Answer 11

that's of course trivial, because we just divided it :-)

so our first two terms in our answer are 6xy^4 - 4x^5y

now we are left with 4xy^2 , and we need to divide that by 4xy^2.

Answer 12

-16x^6y^3

Answer 13

It cancels out

Answer 14

sorry, I said correct, but it wasn't! it should have been -4x^5, not -4x^5y

Answer 15

so our first two terms are 6xy^4 - 4x^5

and we have 4xy^2 divided by 4xy^2 as the part remaining to be done.

Answer 16

It equals one

Answer 17

So the answer is 6xy^4 - 4x^5 + 1

Answer 18

right. and we are left with nothing for the remainder, because after we subtract 1*4xy^2 from 4xy^2, the result is 0.

let's check our answer:
4xy^2 ( 6xy^4 - 4x^5 + 1) = 24x^2y^6 - 16x^6y^2 + 4xy^2
that's what we want to see!

Answer 19

this is an easy case because we only had 1 term in the divisor (4xy^2). we could have done this one just by eyeballing each term and writing down the answer:

24x^2y^6 - 16x^6y^2 + 4xy^2
-------- -------- ----- = 6xy^4 - 4x^5 + 1
4xy^2 4xy^2 4xy^2

Answer 20

often the divisor will have multiple terms, and in that case, the subtraction is a bit more complicated. but you do the same process.

Answer 21

If it has multiple terms, can u just add the terms and then divide the other numbers by it ?

Answer 22

for example,

x^3 + 3x^2 + 3x + 1 divided by x + 1

x^3/ x = x^2, so x^2 is our first term

x^2(x+1) = x^3 + x^2

x^3 + 3x^2 + 3x + 1 - (x^3 + x^2) = 2x^2 + 3x + 1

2x^2 / x = 2x, so 2x is our second term
2x(x+1) = 2x^2 + 2x
2x^2 + 3x + 1 - (2x^2 + 2x) = x + 1

x/x = 1, so 1 is our third term
1(x+1) = x+1
x+1 - (x+1) = 0

so our answer is x^2 + 2x + 1

Answer 23

Thank you, I understand it now

Answer 24

so when doing this, be careful about - signs in the polynomial you are subtracting. I actually prefer to multiply the one being subtracted by -1 and add instead, I just make fewer mistakes that way.

Answer 25

Ok thanks