Question

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

Answer 1

`[4x^2-3x+1]/(x+3) = (4x-15) " remainder " 46`

Explanation:

`color(red)[4x^2-3x+1]/color(blue)(x+3)`

In each line, divide `x` into the term with the highest power of `x`
Write the answer at the top.

`4x^2 div x = 4x`
`" " 4x-15`
`" "x+3bar(|" "color(red)(4x^2 -3x" "+1))`
`color(brown)(4x(x-2)->)" "underline(4x^2+12x)" " larr" Subtract`
`" "0 " "-15x`
`color(brown)(15(x-2))->" "underline(15x-45) larr Subtract`
`color(brown)("Remainder") ->" "0+46`

`:. [4x^2-3x+1]/(x+3) = (4x-15) " remainder " 46`