How do you divide #(x^4+5x^3+6x^2-x-2)-:(x+2)#?

1 Answer
Jim G.
Nov 16, 2017

#x^3+3x^2-1#

Explanation:

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

#"consider the numerator"#

#color(red)(x^3)(x+2)color(magenta)(-2x^3)+5x^3+6x^2-x-2#

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

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

#"quotient "=color(red)(x^3+3x^2-1)," remainder "=0#

#rArr(x^4+5x^3+6x^2-x-2)/(x+2)#

#=(cancel((x+2))(x^3+3x^2-1))/cancel((x+2))=x^3+3x^2-1#

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