How do you divide #( -3x^3+ 6x^2-13x-5 )/(x + 1 )#?

1 Answer
Jim G.
Feb 21, 2018

#-3x^2+9x-22+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)+6x^2-13x-5#

#=color(red)(-3x^2)(x+1)color(red)(+9x)(x+1)color(magenta)(-9x)-13x-5#

#=color(red)(-3x^2)(x+1)color(red)(+9x)(x+1)color(red)(-22)(x+1)color(magenta)(+22)-5#

#=color(red)(-3x^2)(x+1)color(red)(+9x)(x+1)color(red)(-22)(x+1)+17#

#"quotient "=color(red)(-3x^2+9x-22)," remainder "=17#

#rArr(-3x^3+6x^2-13x-5)/(x+1)#

#=-3x^2+9x-22+17/(x+1)#

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