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 May 19th, 2015, 11:51 AM #1 Newbie   Joined: Dec 2013 Posts: 28 Thanks: 0 Can you solve this using algebraic long division? $\frac{ 6x^{3}y-y-5 }{x ^{2}+6y}$ I think I only understand algebraic long division if there's only 1 variable involved. How about this example with 2 variables? I've tried it arranging both dividend and divisor in descending powers of x.The result I get is $6xy+\frac{(-36xy^{2}-y-5)}{(x^{2}+6y)}$ Is this correct?
 May 19th, 2015, 12:09 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 No, it's not- though its close. You can divide one more time. Write the integrand as $6x^3y+ 0x^2y+ 0y^3$- y- 5 $x^2$ divides into that $6xy$ times. Multiplying $x^2+ 6y$ by that gives $6x^3y+ 6x^2y$ and subtracting that from $6x^3y+ 0x^2y+ 0y^3$ leaves $-6x^2y+ 0y^3$. $x^2$ divides into that -6y times. $x^2+ 6y$ times -6y is $-6x^2y- 36 y^2$ and subtracting that from $-6x^2y+ 0y$ leaves 36y^3. $x^2$ will not divide into that so the quotient is $6xy- 6y^2$ with "remainder "$36y^3- y- 5$. $\frac{6x^3y- y- 5}{x^2+ 6y}= 6xy- 6y^2+ \frac{36y^2- y- 5}{x^2+ 6y}$.
 May 20th, 2015, 02:25 AM #3 Senior Member   Joined: May 2015 From: Varanasi Posts: 110 Thanks: 5 Math Focus: Calculus Multiply the exponent of x by 3 giving The answer is x^3 x^3 evaluates to x^3 Multiply x^3 and 6 Multiply x^3 and 1 The x^3 just gets copied along. The answer is x^3 6*x^3 evaluates to 6x^3 Multiply y and x^3 Multiply the y and x^3 Multiply y and x^3 The y just gets copied along. The x^3 just gets copied along. The answer is yx^3 6*x^3*y evaluates to 6yx^3 6*x^3*y-y evaluates to 6yx^3-y The answer is 6yx^3-y-5 6*x^3*y-y-5 evaluates to Multiply the exponent of x by 2giving The answer is x^2 x^2 evaluates to x^2 Multiply y and 6 Multiply y and 1 The y just gets copied along. The answer is y y 6*y evaluates to 6y x^2+6*y evaluates to x^2+6y Sorry, at this time the divisor may be a monomial AT MOST (e.g. contain only 1 term). The answer below IS NOT correct. (6*x^3*y-y-5)/(x^2+6*y) evaluates to 6yx^3-y-5 The final answer is 6yx^3-y-5

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