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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