Divide Using Long Polynomial Division (10x^3+5x^2-1)÷(2x^3-4x^2-x+2)

$(10 x^{3} + 5 x^{2} - 1) \div (2 x^{3} - 4 x^{2} - x + 2)$

Step 1

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

$2 x^{3}$

$4 x^{2}$

$x$

$2$

$10 x^{3}$

$5 x^{2}$

$0 x$

$1$

Step 2

Divide the highest order term in the dividend $10 x^{3}$ by the highest order term in divisor $2 x^{3}$ .

									$5$
	$2 x^{3}$	-	$4 x^{2}$	-	$x$	+	$2$		$10 x^{3}$	+	$5 x^{2}$	+	$0 x$	-	$1$

Step 3

Multiply the new quotient term by the divisor.

$5$

$2 x^{3}$

$4 x^{2}$

$x$

$2$

$10 x^{3}$

$5 x^{2}$

$0 x$

$1$

$10 x^{3}$

$20 x^{2}$

$5 x$

$10$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $10 x^{3} - 20 x^{2} - 5 x + 10$

$5$

$2 x^{3}$

$4 x^{2}$

$x$

$2$

$10 x^{3}$

$5 x^{2}$

$0 x$

$1$

$10 x^{3}$

$20 x^{2}$

$5 x$

$10$

Step 5

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

$5$

$2 x^{3}$

$4 x^{2}$

$x$

$2$

$10 x^{3}$

$5 x^{2}$

$0 x$

$1$

$10 x^{3}$

$20 x^{2}$

$5 x$

$10$

$25 x^{2}$

$5 x$

$11$

Step 6

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

$5 + \frac{25 x^{2} + 5 x - 11}{2 x^{3} - 4 x^{2} - x + 2}$

Divide Using Long Polynomial Division (10x^3+5x^2-1)÷(2x^3-4x^2-x+2)

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