Question

How do you divide `(x^4 + x^3 +1x -1 )/ (x^2 + 1)`?

Answer 1

`x^2+x-1`

Explanation:

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

`"consider the numerator"`

`color(red)(x^2)(x^2+1)color(magenta)(-x^2)+x^3+x-1`

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

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

`"quotient "=color(red)(x^2+x-1)," remainder "=0`

`rArr(x^4+x^3+x-1)/(x^2+1)=x^2+x-1`