How do you divide (4x^3+5x^2-2x-5)/(x^2+4)?

1 Answer
Jim G.
Apr 28, 2017

4x+5-(18x+25)/(x^2+4)

Explanation:

One way is to use the divisor as a factor in the numerator.

color(magenta)"Add/Subtract" terms that are being added/subtracted as a consequence.

"consider the numerator"

color(red)(4x)(x^2+4)color(magenta)(-16x)color(red)(+5)(x^2+4)color(magenta)(-20)-2x-5

=color(red)(4x)(x^2+4)color(red)(+5)(x^2+4)-18x-25

"quotient " =color(red)(4x+5), "remainder " =-(18x+25)

rArr(4x^3+5x^2-2x-5)/(x^2+4)=4x+5-(18x+25)/(x^2+4)

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