How do you divide #(6x^3-12x+10) div (3x-3)#?

2 Answers
Jun 18, 2017

Answer:

#2x^2+2x-2+4/(x-3)#

Explanation:

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

#"consider the numerator"#

#color(red)(2x^2)(3x-3)color(magenta)(+6x^2)-12x+10#

#=color(red)(2x^2)(3x-3)color(red)(+2x)(3x-3)color(magenta)(+6x)-12x+10#

#=color(red)(2x^2)(3x-3)color(red)(+2x)(3x-3)color(red)(-2)(3x-3)color(magenta)(-6)+10#

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

#rArr(6x^3-12x+10)/(3x-3)#

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

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

Jun 18, 2017

Answer:

#color(green)((2x^2+2x-2)+4/(3x-3)#

Explanation:

#(6x^3-12x+10)-:(3x-3)#

# color(white)(.............)ul(color(green)(2x^2+2x-2)#
#color(white)(a)3x-3##|##6x^3+0-12x+10#
#color(white)(...............)ul(6x^3-6x^2)#
#color(white)(........................)6x^2-12x#
#color(white)(........................)ul(6x^2-6x)#
#color(white)(..............................)-6x+10#
#color(white)(...............................)ul(-6x+6)#
#color(white)(.......................................)color(green)(+4#

# color(white)(.............)color(green)((2x^2+2x-2)+4/(3x-3)#