How do you divide #(3x ^ { 3} - 14x ^ { 2} + 16x - 22) \div ( x - 4)#?

1 Answer
Jim G.
Feb 28, 2017

#3x^2-2x+8+10/(x-4)#

Explanation:

This is an alternative approach to the usual long division method.

Using the divisor ( x - 4) as a factor in the numerator.

#color(red)(3x^2)(x-4)color(magenta)(+12x^2)-14x^2+16x-22#

#=color(red)(3x^2)(x-4)color(red)(-2x)(x-4)color(magenta)(-8x)+16x-22#

#=color(red)(3x^2)(x-4)color(red)(-2x)(x-4)color(red)(+8)(x-4)color(magenta)(+32)-22#

#=color(red)(3x^2)(x-4)color(red)(-2x)(x-4)color(red)(+8)(x-4)color(blue)(+10)#

#rArr"quotient " =color(red)(3x^2-2x+8)," remainder "=color(blue)(+10)#

#rArr(3x^3-14x^2+16x-22)/(x-4)=3x^2-2x+8+10/(x-4)#

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