How do you long divide # (x^3-13x -12)/ (x-4)#?

2 Answers
May 31, 2017

The quotient is #=x^2+4x+3# and the remainder is #=0#

Explanation:

Let's perform the long division

#color(white)(aaaa)##x-4##|##color(white)(aaaa)##x^3+0x^2-13x-12##color(white)(aaaa)##|##x^2+4x+3#

#color(white)(aaaaaaaaaaaaaa)##x^3-4x^2#

#color(white)(aaaaaaaaaaaaaaa)##0+4x^2-13x#

#color(white)(aaaaaaaaaaaaaaaaa)##+4x^2-16x#

#color(white)(aaaaaaaaaaaaaaaaaaa)##+0+3x-12#

#color(white)(aaaaaaaaaaaaaaaaaaaaaaa)##+3x-12#

#color(white)(aaaaaaaaaaaaaaaaaaaaaaaaa)##+0-0#

Therefore,

#(x^3-13x-12)/(x-4)=x^2+4x+3#

May 31, 2017

#x^2+4x+3#

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-12#

#=color(red)(x^2)(x-4)color(red)(+4x)(x-4)color(magenta)(+16x)-13x-12#

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

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

#"quotient "=color(red)(x^2+4x+3)," remainder "=0#

#rArr(x^3-13x-12)/(x-4)=x^2+4x+3#