How do you divide #( x^3+4x^2-17x-16 )/(x-4)#?

1 Answer
Jim G.
Apr 20, 2018

#x^2+8x+15+44/(x-4)#

Explanation:

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

#"consider the numerator"#

#color(red)(x^2)(x-4)color(magenta)(+4x^2)+4x^2-17x-16#

#=color(red)(x^2)(x-4)color(red)(+8x)(x-4)color(magenta)(+32x)-17x-16#

#=color(red)(x^2)(x-4)color(red)(+8x)(x-4)color(red)(+15)(x-4)color(magenta)(+60)-16#

#=color(red)(x^2)(x-4)color(red)(+8x)(x-4)color(red)(+15)(x-4)+44#

#"quotient "=color(red)(x^2+8x+15)," remainder "=44#

#rArr(x^3+4x^2-17x-16)/(x-4)#

#=x^2+8x+15+44/(x-4)#

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