Question

How do you long divide `(x^4 + a^4) / (x^2 + a^2)`?

Answer 1

Quotient is `x^2-a^2` and remainder is `2a^4`

Explanation:

`" "x^4+0x^3+0x^2+0x+a^4`
`color(magenta)(x^2)(x^2+a^2) ->color(white)(X)ul(x^4+0x^3+a^2x^2) larr" Subtract"`
`" "0color(white)(XXX)-a^2x^2+0x+a^4`
`color(magenta)(-a^2)(x^2+a^2)->" "color(white)(XXX)ul(-a^2x^2-0x-a^4) larr" Subtract"`
`" "2a^4`

Hence, quotient is `x^2-a^2` and remainder is `2a^4`