How do you divide #(x^3 - 12x^2 -5x + 6)/(x-2)#?

1 Answer
Jim G.
May 16, 2017

#x^2-10x-25-44/(x-2)#

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)-12x^2-5x+6#

#=color(red)(x^2)(x-2)color(red)(-10x)(x-2)color(magenta)(-20x)-5x+6#

#=color(red)(x^2)(x-2)color(red)(-10x)(x-2)color(red)(-25)(x-2)color(magenta)(-50)+6#

#=color(red)(x^2)(x-2)color(red)(-10x)(x-2)color(red)(-25)(x-2)-44#

#rArr"quotient "=color(red)(x^2-10x-25)," remainder "=-44#

#rArr(x^3-12x^2-5x+6)/(x-2)=x^2-10x-25-44/(x-2)#

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