SOLUTION: find the following quotient:
3x^2-25y^2/3x+5y
I did this and got x-5y, I then checked it on a math site with calculator and
it said the answer was x with a remainder of 0. h
Algebra.Com
Question 486078: find the following quotient:
3x^2-25y^2/3x+5y
I did this and got x-5y, I then checked it on a math site with calculator and
it said the answer was x with a remainder of 0. how am I wrong?????
because I did another one x^2-36/x+6 and got x-6 which was correct.
doesn't the same apply to the first one. Thanks for any input.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Well, 
is the quotient although it is an incomplete answer because there is a remainder involved. 
remainder 0 is completely out to lunch. ((3x\ -\ 5y)\ =\ 3x^2\ -\ 5xy\ \neq\ 3x^2\ -\ 25y^2)
)
The reason 
comes out so tidily is NOT because "x goes in to x-squared x times and 6 goes into 36 six times" but rather because of the factorization of the numerator. Note that the numerator is the difference of two squares, so
(x\ -\ 6)}{x\ +\ 6}\ =\ x\ -\ 6,\ x\ \neq\ -6)
Considering the number 3 to be the square of 
, you can factor the numerator of your problem as the difference of two squares:
x\ -\ 5y\right)\left(\left(\sqrt{3}\right)x\ +\ 5y\right))
but neither of these factors is evenly divisible by your given denominator, 
The only thing left to us is to do multi-variable polynomial long division. A process that is very difficult and time consuming to render on this system. Perhaps you can get an idea from:
MathIsFun Polynomial Long Division (scroll all the way down to the bottom of the page for the multi-variable process)
Properly performed you should obtain the quotient that you mentioned, but also with a remainder of 
In summary:
John
My calculator said it, I believe it, that settles it
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