Question

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

Answer 1

`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)`