How do you divide (3x^3 - 12x^2 - 11x - 20)/(x+5)?

2 Answers
Dec 24, 2017

(3x^3−12x^2−11x−20)/(x+5)=3x^2-27x+124-640/(x+5)

Explanation:

(3x^3−12x^2−11x−20)-:(x+5)=3x^2-27x+124
(3x^3+15x^2)/
color(white)(..)0-27x^2-11x-20
color(white)(....)(-27x^2-135x)/
color(white)(...........)0+124x-20
color(white)(..............)(+124x+620)/
color(white)(......................)0-640

(3x^3−12x^2−11x−20)/(x+5)=3x^2-27x+124+(-640)/(x+5)

Dec 24, 2017

3x^2-27x+124-640/(x+5)

Explanation:

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

"consider the numerator"

color(red)(3x^2)(x+5)color(magenta)(-15x^2)-12x^2-11x-20

=color(red)(3x^2)(x+5)color(red)(-27x)(x+5)color(magenta)(+135x)-11x-20

=color(red)(3x^2)(x+5)color(red)(-27x)(x+5)color(red)(+124)(x+5)color(magenta)(-620)-20

=color(red)(3x^2)(x+5)color(red)(-27x)(x+5)color(red)(+124)(x+5)-640

"quotient "=color(red)(3x^2-27x+124)," remainder "=-640

rArr(3x^3-12x^2-11x-20)/(x+5)

=3x^2-27x+124-640/(x+5)