How do you divide #(x ^ { 3} - 3x ^ { 2} - 2) -: ( x + 2)#?

1 Answer
Jim G.
Jan 1, 2018

#x^2-5x+10-22/(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^2-2#

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

#=color(red)(x^2)(x+2)color(red)(-5x)(x+2)color(red)(+10)(x+2)color(magenta)(-20)-2#

#=color(red)(x^2)(x+2)color(red)(-5x)(x+2)color(red)(+10)(x+2)-22#

#"quotient "=color(red)(x^2-5x+10)," remainder "=-22#

#rArr(x^3-3x^2-2)/(x+2)=x^2-5x+10-22/(x+2)#

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