How do you divide #(6x ^ { 3} y ^ { 3} - 11x ^ { 2} y ^ { 2} + 18x y - 5) \div ( 3x y - 1)#?

1 Answer
Jim G.
Jul 7, 2017

#2x^2y^2-3xy+5#

Explanation:

#"one way is to use the divisor as a factor in the numerator"#

#"consider the numerator"#

#color(red)(2x^2y^2)(3xy-1)color(magenta)(+2x^2y^2)-11x^2y^2+18xy-5#

#=color(red)(2x^2y^2)(3xy-1)color(red)(-3xy)(3xy-1)color(magenta)(-3xy)+18xy-5#

#=color(red)(2x^2y^2)(3xy-1)color(red)(-3xy)(3xy-1)color(red)(+5)(3xy-1)color(magenta)(+5)-5#

#=color(red)(2x^2y^2)(3xy-1)color(red)(-3xy)(3xy-1)color(red)(+5)(3xy-1)+0#

#"quotient "=color(red)(2x^2y^2-3xy+5)," remainder "=0#

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