How do you divide #(4x^4 -5x^2-2x+24)/((x + 4) )#?

1 Answer
Jim G.
Oct 6, 2017

#4x^3-16x^2+59x-238+976/(x+4)#

Explanation:

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

#"consider the numerator"#

#color(red)(4x^3)(x+4)color(magenta)(-16x^3)-5x^2-2x+24#

#=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(magenta)(+64x^2)-5x^2-2x+24#

#=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(red)(+59x)(x+4)color(magenta)(-236x)-2x+24#

#=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(red)(+59x)(x+4)color(red)#
#color(white)(=)color(red)(-238)(x+4)color(magenta)(+952)+24#

#"quotient "=color(red)(4x^3-16x^2+59x-238)#

#"remainder "=976#

#rArr(4x^4-5x^2-2x+24)/(x+4)#

#=4x^3-16x^2+59x-238+976/(x+4)#

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