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

1 Answer
Jim G.
Apr 12, 2017

#x^2+4x+5+5/(x-2)#

Explanation:

One way is to use the divisor x - 2 as a factor in the numerator.

#"Consider the numerator"#

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

#=color(red)(x^2)(x-2)color(red)(+4x)(x-2)color(red)(+8x)-3x-5#

#=color(red)(x^2)(x-2)color(red)(+4x)(x-2)color(red)(+5)(x-2)color(red)(+10)-5#

#=color(red)(x^2)(x-2)color(red)(+4x)(x-2)color(red)(+5)(x-2)+5#

#rArr(x^3+2x^2-3x-5)/(x-2)=color(red)(x^2+4x+5)+5/(x-2)#

#"quotient is " x^2+4x+5" and remainder " =5#

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