Question

What is the quotient of `(x^3+3x^2-3x-12)div(x^2+5x+6)`?

Answer 1

`x-2`

Explanation:

One way of dividing a rational function is to use the divisor as a factor in the numerator.

`"Consider the numerator"`

`color(red)(x)(x^2+5x+6)color(magenta)(-5x^2-6x)+3x^2-3x-12`

`=color(red)(x)(x^2+5x+6)color(red)(-2)(x^2+5x+6)color(magenta)(+10x+12)-9x-12`

`=color(red)(x)(x^2+5x+6)color(red)(-2)(x^2+5x+6)+x`

`"quotient is " color(red)(x-2)" and remainder is " x`

`rArr(x^3+3x^2-3x-12)/(x^2+5x+6)=x-2+x/(x^2+5x+6)`