Divide Using Long Polynomial Division (8x^3-3x+1)÷(4x^3+x^2-2x-3)

$(8 x^{3} - 3 x + 1) \div (4 x^{3} + x^{2} - 2 x - 3)$

Step 1

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

$4 x^{3}$

$x^{2}$

$2 x$

$3$

$8 x^{3}$

$0 x^{2}$

$3 x$

$1$

Step 2

Divide the highest order term in the dividend $8 x^{3}$ by the highest order term in divisor $4 x^{3}$ .

									$2$
	$4 x^{3}$	+	$x^{2}$	-	$2 x$	-	$3$		$8 x^{3}$	+	$0 x^{2}$	-	$3 x$	+	$1$

Step 3

Multiply the new quotient term by the divisor.

$2$

$4 x^{3}$

$x^{2}$

$2 x$

$3$

$8 x^{3}$

$0 x^{2}$

$3 x$

$1$

$8 x^{3}$

$2 x^{2}$

$4 x$

$6$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $8 x^{3} + 2 x^{2} - 4 x - 6$

$2$

$4 x^{3}$

$x^{2}$

$2 x$

$3$

$8 x^{3}$

$0 x^{2}$

$3 x$

$1$

$8 x^{3}$

$2 x^{2}$

$4 x$

$6$

Step 5

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

$2$

$4 x^{3}$

$x^{2}$

$2 x$

$3$

$8 x^{3}$

$0 x^{2}$

$3 x$

$1$

$8 x^{3}$

$2 x^{2}$

$4 x$

$6$

$2 x^{2}$

$x$

$7$

Step 6

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

$2 + \frac{- 2 x^{2} + x + 7}{4 x^{3} + x^{2} - 2 x - 3}$

Divide Using Long Polynomial Division (8x^3-3x+1)÷(4x^3+x^2-2x-3)

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