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

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

Step 1

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

$x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{3}$

$3 x^{2}$

$2 x$

$6$

Step 2

Divide the highest order term in the dividend $5 x^{3}$ by the highest order term in divisor $x^{3}$ .

$5$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{3}$

$3 x^{2}$

$2 x$

$6$

Step 3

Multiply the new quotient term by the divisor.

$5$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

$5 x^{3}$

$3 x^{2}$

$2 x$

$6$

$5 x^{3}$

$0$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $5 x^{3} + 0 + 0 + 0$

Step 5

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Step 6

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

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