How do you divide #(x ^ { 3} - 3x ^ { 2} - 2) -: ( x + 2)#?
1 Answer
Jan 1, 2018
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)#