How do you divide (4x^4 -5x^2-2x+24)/((x + 4) )4x4−5x2−2x+24(x+4)?

1 Answer
Jim G.
Oct 6, 2017

4x^3-16x^2+59x-238+976/(x+4)4x3−16x2+59x−238+976x+4

Explanation:

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

"consider the numerator"consider the numerator

color(red)(4x^3)(x+4)color(magenta)(-16x^3)-5x^2-2x+244x3(x+4)−16x3−5x2−2x+24

=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(magenta)(+64x^2)-5x^2-2x+24=4x3(x+4)−16x2(x+4)+64x2−5x2−2x+24

=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(red)(+59x)(x+4)color(magenta)(-236x)-2x+24=4x3(x+4)−16x2(x+4)+59x(x+4)−236x−2x+24

=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(red)(+59x)(x+4)color(red)=4x3(x+4)−16x2(x+4)+59x(x+4)
color(white)(=)color(red)(-238)(x+4)color(magenta)(+952)+24=−238(x+4)+952+24

"quotient "=color(red)(4x^3-16x^2+59x-238)quotient =4x3−16x2+59x−238

"remainder "=976remainder =976

rArr(4x^4-5x^2-2x+24)/(x+4)⇒4x4−5x2−2x+24x+4

=4x^3-16x^2+59x-238+976/(x+4)=4x3−16x2+59x−238+976x+4

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