How do you divide #(x^3-13x-18) / (x-4) #?

1 Answer
Jim G.
Aug 8, 2017

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

Explanation:

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

#"consider the numerator"#

#color(red)(x^2)(x-4)color(magenta)(+4x^2)-13x-18#

#=color(red)(x^2)(x-4)color(red)(+4x)(x-4)color(magenta)(+16x)-13x-18#

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

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

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

#rArr(x^3-13x-18)/(x-4)=x^2+4x+3-6/(x-4)#

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