How do you evaluate #(x ^ { 3} + 3x ^ { 2} - 2x - 5) \div ( x - 2)#?

1 Answer
Jim G.
Nov 13, 2017

#x^2+5x+8+11/(x-2)#

Explanation:

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

#"consider the numerator"#

#color(red)(x^2)(x-2)color(magenta)(+2x^2)+3x^2-2x-5#

#=color(red)(x^2)(x-2)color(red)(+5x)(x-2)color(magenta)(+10x)-2x-5#

#=color(red)(x^2)(x-2)color(red)(+5x)(x-2)color(red)(+8)(x-2)color(magenta)(+16)-5#

#=color(red)(x^2)(x-2)color(red)(+5x)(x-2)color(red)(+8)(x-2)+11#

#"quotient "=color(red)(x^2+5x+8)," remainder "=+11#

#rArr(x^3+3x^2-2x-5)/(x-2)#

#=x^2+5x+8+11/(x-2)#

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