Question

What Is `(x^3+x^2-5x+6)/(x+1)`? Help, Please?

Answer 1

`x^2-5+11/(x+1)`

Explanation:

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

`"consider the numerator"`

`color(red)(x^2)(x+1)cancel(color(magenta)(-x^2))cancel(+x^2)-5x+6`

`=color(red)(x^2)(x+1)color(red)(-5)(x+1)color(magenta)(+5)+6`

`=color(red)(x^2)(x+1)color(red)(-5)(x+1)+11`

`"quotient "=color(red)(x^2-5)" remainder "=11`

`(x^3+x^2-5x+6)/(x+1)=x^2-5+11/(x+1)`