Question

How do you divide `(x-5x^2+10+x^3)/(x+2)`?

Answer 1

`x^2-7x+15-20/(x+2)`

Explanation:

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

`"consider the rearranged numerator"`

`x^3-5x^2+x+10`

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

`=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(magenta)(+14x)+x+10`

`=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(red)(+15)(x+2)color(magenta)(-30)+10`

`=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(red)(+15)(x+2)-20`

`"quotient "=color(red)(x^2-7x+15)," remainder "=-20`

`(x-5x^2+10+x^3)/(x+2)=x^2-7x+15-20/(x+2)`