Finite Math Examples

f (x) = x^{2} + 2 x + 1

$f (x) = x^{2} + 2 x + 1$ ,

x = 2

$x = 2$

Step 1

Set up the long division problem to evaluate the function at

2

$2$ .

\frac{x^{2} + 2 x + 1}{x - (2)}

$\frac{x^{2} + 2 x + 1}{x - (2)}$

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.

$2$ $2$	$1$ $1$	$2$ $2$	$1$ $1$

Step 2.2

The first number in the dividend

(1)

$(1)$ is put into the first position of the result area (below the horizontal line).

$2$ $2$	$1$ $1$	$2$ $2$	$1$ $1$

	$1$ $1$

Step 2.3

Multiply the newest entry in the result

(1)

$(1)$ by the divisor

(2)

$(2)$ and place the result of

(2)

$(2)$ under the next term in the dividend

(2)

$(2)$ .

$2$ $2$	$1$ $1$	$2$ $2$	$1$ $1$
		$2$ $2$
	$1$ $1$

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.

$2$ $2$	$1$ $1$	$2$ $2$	$1$ $1$
		$2$ $2$
	$1$ $1$	$4$ $4$

Step 2.5

Multiply the newest entry in the result

(4)

$(4)$ by the divisor

(2)

$(2)$ and place the result of

(8)

$(8)$ under the next term in the dividend

(1)

$(1)$ .

$2$ $2$	$1$ $1$	$2$ $2$	$1$ $1$
		$2$ $2$	$8$ $8$
	$1$ $1$	$4$ $4$

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.

$2$ $2$	$1$ $1$	$2$ $2$	$1$ $1$
		$2$ $2$	$8$ $8$
	$1$ $1$	$4$ $4$	$9$ $9$

Step 2.7

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

(1) x + 4 + \frac{9}{x - 2}

$(1) x + 4 + \frac{9}{x - 2}$

Step 2.8

Simplify the quotient polynomial.

x + 4 + \frac{9}{x - 2}

$x + 4 + \frac{9}{x - 2}$

x + 4 + \frac{9}{x - 2}

$x + 4 + \frac{9}{x - 2}$

Step 3

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

9

$9$

Step 4

Since the remainder is not equal to zero,

x = 2

$x = 2$ is not a factor.

x = 2

$x = 2$ is not a factor

Step 5

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