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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? 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 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  y 5 divides into that times. Multiplying by that gives and subtracting that from leaves . divides into that 6y times. times 6y is and subtracting that from leaves 36y^3. will not divide into that so the quotient is with "remainder ". . 
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*yy evaluates to 6yx^3y The answer is 6yx^3y5 6*x^3*yy5 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*yy5)/(x^2+6*y) evaluates to 6yx^3y5 The final answer is 6yx^3y5 

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