How do you evaluate #(x^{3}+8x^{2}+2x-11)\div (x-2)#?

2 Answers
Teun
Jan 27, 2018

Using long division.

Explanation:

It is hard to show how long division works in this applet. So I would recommend looking it up on another website like khanacademy where they illustrate the method for you.

Jim G.
Jan 27, 2018

#x^2+10x+22+33/(x-2)#

Explanation:

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

#"consider the numerator"#

#color(red)(x^2)(x-2)color(magenta)(+2x^2)+8x^2+2x-11#

#=color(red)(x^2)(x-2)color(red)(+10x)(x-2)color(magenta)(+20x)+2x-11#

#=color(red)(x^2)(x-2)color(red)(+10x)(x-2)color(red)(+22)(x-2)color(magenta)(+44)-11#

#=color(red)(x^2)(x-2)color(red)(+10x)(x-2)color(red)(+22)(x-2)+33#

#"quotient "=color(red)(x^2+10x+22)," remainder "=33#

#rArr(x^3+8x^2+2x-11)/(x-2)#

#=x^2+10x+22+33/(x-2)#

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