Question

How do you divide `(x^3-13x-18) / (x-4)`?

Answer 1

`x^2+4x+3-6/(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)-13x-18`

`=color(red)(x^2)(x-4)color(red)(+4x)(x-4)color(magenta)(+16x)-13x-18`

`=color(red)(x^2)(x-4)color(red)(+4x)(x-4)color(red)(+3)(x-4)color(magenta)(+12)-18`

`=color(red)(x^2)(x-4)color(red)(+4x)(x-4)color(red)(+3)(x-4)-6`

`"quotient "=color(red)(x^2+4x+3)," remainder "=-6`

`rArr(x^3-13x-18)/(x-4)=x^2+4x+3-6/(x-4)`