Algebra Examples

$\frac{5 x^{2} - 6 x + 10 x - 2}{15 x^{3} + 2 x}$

Step 1

To calculate the remainder, first divide the polynomials.

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Step 1.1

Add $- 6 x$ and $10 x$ .

$\frac{5 x^{2} + 4 x - 2}{15 x^{3} + 2 x}$

Step 1.2

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

$15 x^{3}$

$0 x^{2}$

$2 x$

$0$

$5 x^{2}$

$4 x$

$2$

Step 1.3

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

$0 + \frac{15 x^{3} + 5 x^{2} + 6 x - 2}{15 x^{3} + 2 x}$

Step 2

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

$15 x^{3} + 5 x^{2} + 6 x - 2$