How do you divide #( -3x^3+ 15x^2-x-2)/(x + 1 )#?

1 Answer
Jim G.
Jun 19, 2017

#-3x^2+18x-19+17/(x+1)#

Explanation:

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

#"consider the numerator"#

#color(red)(-3x^2)(x+1)color(magenta)(+3x^2)+15x^2-x-2#

#=color(red)(-3x^2)(x+1)color(red)(+18x)(x+1)color(magenta)(-18x)-x-2#

#=color(red)(-3x^2)(x+1)color(red)(+18x)(x+1)color(red)(-19)(x+1)color(magenta)(+19)-2#

#rArr(-3x^3+15x^2-x-2)/(x+1)#

#=(cancel((x+1))(color(red)(-3x^2+18x-19)))/cancel((x+1))+17/(x+1)#

#=-3x^2+18x-19+17/(x+1)#

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