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 ->  Polynomials-and-rational-expressions -> 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      Log On


   



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) About Me  (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. ()

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



Considering the number 3 to be the square of , you can factor the numerator of your problem as the difference of two squares:




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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