How do you divide #(9x ^ { 3} + 3x ^ { 2} + 6x - 18) \div ( 3x - 3)#?

1 Answer
Jim G.
Aug 8, 2017

#3x^2+4x+6#

Explanation:

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

#"consider the numerator"#

#color(red)(3x^2)(3x-3)color(magenta)(+9x^2)+3x^2+6x-18#

#=color(red)(3x^2)(3x-3)color(red)(+4x)(3x-3)color(magenta)(+12x)+6x-18#

#=color(red)(3x^2)(3x-3)color(red)(+4x)(3x-3)color(red)(+6)(3x-3)color(magenta)(+18)-18#

#=color(red)(3x^2)(3x-3)color(red)(+4x)(3x-3)color(red)(+6)(3x-3)+0#

#"quotient "=color(red)(3x^2+4x+6)," remainder "=0#

#rArr(cancel((3x-3))(3x^2+4x+6))/cancel((3x-3))=3x^2+4x+6#

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