Precalculus Examples

$\frac{x - 1}{x^{5} - 2 x^{3} + x^{2} - 4}$

Step 1

To calculate the remainder, first divide the polynomials.

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Step 1.1

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

$x^{5}$

$0 x^{4}$

$2 x^{3}$

$x^{2}$

$0 x$

$4$

$x$

$1$

Step 1.2

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

$0 + \frac{x^{5} - 2 x^{3} + x^{2} + x - 5}{x^{5} - 2 x^{3} + x^{2} - 4}$

Step 2

Since the last term in the resulting expression is a fraction, the numerator of the fraction is the remainder.

$x^{5} - 2 x^{3} + x^{2} + x - 5$