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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