Precalculus Examples

\frac{6 x^{2} + 5 x - 7}{x + 2}

$\frac{6 x^{2} + 5 x - 7}{x + 2}$

Step 1

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

$- 2$ $- 2$	$6$ $6$	$5$ $5$	$- 7$ $- 7$

Step 2

The first number in the dividend

(6)

$(6)$ is put into the first position of the result area (below the horizontal line).

Step 3

Multiply the newest entry in the result

(6)

$(6)$ by the divisor

(- 2)

$(- 2)$ and place the result of

(- 12)

$(- 12)$ under the next term in the dividend

(5)

$(5)$ .

Step 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.

Step 5

Multiply the newest entry in the result

(- 7)

$(- 7)$ by the divisor

(- 2)

$(- 2)$ and place the result of

(14)

$(14)$ under the next term in the dividend

(- 7)

$(- 7)$ .

Step 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.

Step 7

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

(6) x - 7 + \frac{7}{x + 2}

$(6) x - 7 + \frac{7}{x + 2}$

Step 8

Simplify the quotient polynomial.

6 x - 7 + \frac{7}{x + 2}

$6 x - 7 + \frac{7}{x + 2}$

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