Question

How do you solve `(x^ { 3} - 4x ^ { 2} - 11x + 30 )\div (x - 2)?`

Answer 1

`color(green)(x^2 -2x -15)`

Explanation:

`color(white)(aaaa)2color(white)(aa)|color(white)(aa)1color(white)(aa)-4color(white)(aa)-11color(white)(aa)30`

`color(white)(aaaaaaaaaa)darrcolor(white)(aaaa)2color(white)(aa)-4color(white)()-30`

`color(white)(aaaaaaa)---------`

`color(white)(aaaaaaaaaaa)1color(white)(aa)-2color(white)(aa)-15color(white)(aa)0`

`x^2 -2x -15`

Answer 2

`x^2-2x-15`

Explanation:

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

`"consider the numerator"`

`color(red)(x^2)(x-2)color(magenta)(+2x^2)-4x^2-11x+30`

`=color(red)(x^2)(x-2)color(red)(-2x)(x-2)color(magenta)(-4x)-11x+30`

`=color(red)(x^2)(x-2)color(red)(-2x)(x-2)color(red)(-15)(x-2)color(magenta)(-30)+30`

`=color(red)(x^2)(x-2)color(red)(-2x)(x-2)color(red)(-15)(x-2)+0`

`"quotient "=color(red)(x^2-2x-15)," remainder" =0`

`rArr(x^3-4x^2-11x+30)/(x-2)=x^2-2x-15`