Question

Divide.
X³+2x²-x+1/x^2+2
Show steps

Answer 1

( x + 2 ) + ( -3x - 3)/(x + 2)

Explanation:

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

= ( x + 2 ) + ( -3x - 3)/(x + 2)

I solved this problem by long division, so I do know how to explain it here but if you have any questions, you can ask me in the comments.

Answer 2

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

Explanation:

As the divisor is quadratic, use long division rather than synthetic division:

`\large \begin{array}{r}x+2\phantom{)}\\x^2+2{\overline{\smash{\big)}\,x^3+2x^2-x+1\phantom{)}}}\\{-~\phantom{(}\underline{(x^3\phantom{))))))}+2x)\phantom{-b)}}\\2x^2-3x+1\phantom{)}\\-~\phantom{()}\underline{(2x^2\phantom{))))))}+4)\phantom{}}\\-3x-3\phantom{)}\\\end{array}`

Therefore:

`\textsf{Dividend}: \quad x^3+2x^2-x+1`

`\textsf{Divisor}: \quad x^2+2`

`\textsf{Quotient}: \quad x+2`

`\textsf{Remainder}: \quad -3x-x=-(3x+x)`

When dividing a polynomial, the result is the quotient plus the remainder over the divisor.

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