Question

How do you divide `(x^3 - 12x^2 -5x + 6)/(x-2)`?

Answer 1

`x^2-10x-25-44/(x-2)`

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)-12x^2-5x+6`

`=color(red)(x^2)(x-2)color(red)(-10x)(x-2)color(magenta)(-20x)-5x+6`

`=color(red)(x^2)(x-2)color(red)(-10x)(x-2)color(red)(-25)(x-2)color(magenta)(-50)+6`

`=color(red)(x^2)(x-2)color(red)(-10x)(x-2)color(red)(-25)(x-2)-44`

`rArr"quotient "=color(red)(x^2-10x-25)," remainder "=-44`

`rArr(x^3-12x^2-5x+6)/(x-2)=x^2-10x-25-44/(x-2)`