Algebra Examples

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

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

x = 1

$x = 1$

Step 1

Set up the long division problem to evaluate the function at

1

$1$ .

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

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

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.

$1$ $1$	$1$ $1$	$0$ $0$	$- 1$ $- 1$

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).

$1$ $1$	$1$ $1$	$0$ $0$	$- 1$ $- 1$

	$1$ $1$

Step 2.3

Multiply the newest entry in the result

(1)

$(1)$ by the divisor

(1)

$(1)$ and place the result of

(1)

$(1)$ under the next term in the dividend

(0)

$(0)$ .

$1$ $1$	$1$ $1$	$0$ $0$	$- 1$ $- 1$
		$1$ $1$
	$1$ $1$

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.

$1$ $1$	$1$ $1$	$0$ $0$	$- 1$ $- 1$
		$1$ $1$
	$1$ $1$	$1$ $1$

Step 2.5

Multiply the newest entry in the result

(1)

$(1)$ by the divisor

(1)

$(1)$ and place the result of

(1)

$(1)$ under the next term in the dividend

(- 1)

$(- 1)$ .

$1$ $1$	$1$ $1$	$0$ $0$	$- 1$ $- 1$
		$1$ $1$	$1$ $1$
	$1$ $1$	$1$ $1$

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.

$1$ $1$	$1$ $1$	$0$ $0$	$- 1$ $- 1$
		$1$ $1$	$1$ $1$
	$1$ $1$	$1$ $1$	$0$ $0$

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 + 1

$(1) x + 1$

Step 2.8

Simplify the quotient polynomial.

x + 1

$x + 1$

x + 1

$x + 1$

Step 3

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

0

$0$

Step 4

Since the remainder is equal to zero,

x = 1

$x = 1$ is a factor.

x = 1

$x = 1$ is a factor

Step 5

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