How do you divide #(x-5x^2+10+x^3)/(x+2)#?

1 Answer
Jim G.
Jul 14, 2018

#x^2-7x+15-20/(x+2)#

Explanation:

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

#"consider the rearranged numerator"#

#x^3-5x^2+x+10#

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

#=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(magenta)(+14x)+x+10#

#=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(red)(+15)(x+2)color(magenta)(-30)+10#

#=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(red)(+15)(x+2)-20#

#"quotient "=color(red)(x^2-7x+15)," remainder "=-20#

#(x-5x^2+10+x^3)/(x+2)=x^2-7x+15-20/(x+2)#

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