Question

How do you simplify and divide `(x^4+x^2-3x+5)/(x^2+2)`?

Answer 1

`x^2-1+(7-3x)/(x^2+2)`

Explanation:

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

`"consider the numerator"`

`color(red)(x^2)(x^2+2)color(magenta)(-2x^2)+x^2-3x+5`

`=color(red)(x^2)(x^2+2)color(red)(-1)(x^2+2)color(magenta)(+2)-3x+5`

`=color(red)(x^2)(x^2+2)color(red)(-1)(x^2+2)+7-3x`

`rArr(x^4+x^2-3x+5)/(x^2+2)`

`=x^2-1+(7-3x)/(x^2+2)`