Divide Using Long Polynomial Division (x^5+12x^3-5x)/(2x^6+4x^3+x^2-2)

$\frac{(x^{5} + 12 x^{3} - 5 x)}{2 x^{6} + 4 x^{3} + x^{2} - 2}$

Step 1

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

$2 x^{6}$

$0 x^{5}$

$0 x^{4}$

$4 x^{3}$

$x^{2}$

$0 x$

$2$

$x^{5}$

$0 x^{4}$

$12 x^{3}$

$0 x^{2}$

$5 x$

$0$

Step 2

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

$0 + \frac{2 x^{6} + 16 x^{3} + x^{2} - 2 + x^{5} - 5 x}{2 x^{6} + 4 x^{3} + x^{2} - 2}$