Algebra Examples

$\frac{- 18 x^{2} - 6 x + 12}{3 x^{3} + 9 x - 1}$

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 $0$ .

$3 x^{3}$

$0 x^{2}$

$9 x$

$1$

$18 x^{2}$

$6 x$

$12$

Step 1.2

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

$0 + \frac{3 x^{3} + 3 x - 18 x^{2} + 11}{3 x^{3} + 9 x - 1}$

Step 2

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

$3 x^{3} + 3 x - 18 x^{2} + 11$