How do you divide #(3x ^ { 3} + 22x ^ { 2} - 13x + 23) \div ( x + 8)#?

1 Answer
Jim G.
Sep 17, 2017

#3x^2-2x+3-1/(x+8)#

Explanation:

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

#"consider the numerator"#

#color(red)(3x^2)(x+8)color(magenta)(-24x^2)+22x^2-13x+23#

#=color(red)(3x^2)(x+8)color(red)(-2x)(x+8)color(magenta)(+16x)-13x+23#

#=color(red)(3x^2)(x+8)color(red)(-2x)(x+8)color(red)(+3)(x+8)color(magenta)(-24)+23#

#=color(red)(3x^2)(x+8)color(red)(-2x)(x+8)color(red)(+3)(x+8)-1#

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

#rArr(3x^3+22x^2-13x+23)/(x+8)=3x^2-2x+3-1/(x+8)#

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