How do you divide #(15x ^ { 3} + 37x ^ { 2} + 53x + 55) \div ( 3x + 5)#?

1 Answer
Jim G.
Sep 27, 2017

#5x^2+4x+11#

Explanation:

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

#"consider the numerator"#

#color(red)(5x^2)(3x+5)color(magenta)(-25x^2)+37x^2+53x+55#

#=color(red)(5x^2)(3x+5)color(red)(+4x)(3x+5)color(magenta)(-20x)+53x+55#

#=color(red)(5x^2)(3x+5)color(red)(+4x)(3x+5)color(red)(+11)(3x+5)color(magenta)(-55)+55#

#=color(red)(5x^2)(3x+5)color(red)(+4x)(3x+5)color(red)(+11)(3x+5)+0#

#rArr(15x^3+37x^2+53x+55)/(3x+5)#

#=(cancel((3x+5))(5x^2+4x+11))/cancel((3x+5))=5x^2+4x+11#

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