How do you divide #(x^3-13x-18) / (x-4) #?
1 Answer
Aug 8, 2017
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)#