Precalculus Examples

$f (x) = 4 x^{3}$ ,

$x = 0$

Step 1

Set up the long division problem to evaluate the function at

$0$ .

$\frac{4 x^{3}}{x - (0)}$

Step 2

Divide using synthetic division.

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Step 2.1

Place the numbers representing the divisor and the dividend into a division-like configuration.

$0$	$4$	$0$	$0$	$0$

Step 2.2

The first number in the dividend

$(4)$ is put into the first position of the result area (below the horizontal line).

$0$	$4$	$0$	$0$	$0$

	$4$

Step 2.3

Multiply the newest entry in the result

$(4)$ by the divisor

$(0)$ and place the result of

$(0)$ under the next term in the dividend

$(0)$ .

$0$	$4$	$0$	$0$	$0$
		$0$
	$4$

Step 2.4

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$0$	$4$	$0$	$0$	$0$
		$0$
	$4$	$0$

Step 2.5

Multiply the newest entry in the result

$(0)$ by the divisor

$(0)$ and place the result of

$(0)$ under the next term in the dividend

$(0)$ .

$0$	$4$	$0$	$0$	$0$
		$0$	$0$
	$4$	$0$

Step 2.6

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$0$	$4$	$0$	$0$	$0$
		$0$	$0$
	$4$	$0$	$0$

Step 2.7

Multiply the newest entry in the result

$(0)$ by the divisor

$(0)$ and place the result of

$(0)$ under the next term in the dividend

$(0)$ .

$0$	$4$	$0$	$0$	$0$
		$0$	$0$	$0$
	$4$	$0$	$0$

Step 2.8

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$0$	$4$	$0$	$0$	$0$
		$0$	$0$	$0$
	$4$	$0$	$0$	$0$

Step 2.9

All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.

$4 x^{2} + 0 x + 0$

Step 2.10

Simplify the quotient polynomial.

$4 x^{2}$

Step 3

The remainder of the synthetic division is the result based on the remainder theorem.

$0$

Step 4

Since the remainder is equal to zero,

$x = 0$ is a factor.

$x = 0$ is a factor

Step 5

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