Precalculus Examples

$\frac{x^{2} + x - 1}{x^{5} + x^{4} - 2 x^{2} + x + 1}$

Step 1

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$x^{5}$

$x^{4}$

$0 x^{3}$

$2 x^{2}$

$x$

$1$

$x^{2}$

$x$

$1$

Step 2

The final answer is the quotient plus the remainder over the divisor.

$0 + \frac{x^{5} + x^{4} - x^{2} + 2 x}{x^{5} + x^{4} - 2 x^{2} + x + 1}$