Algebra Examples

$\frac{x^{2} + x - 30}{x - 5}$

Step 1

Factor

$x^{2} + x - 30$ using the AC method.

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Step 1.1

Consider the form

$x^{2} + b x + c$ . Find a pair of integers whose product is

$c$ and whose sum is

$b$ . In this case, whose product is

$- 30$ and whose sum is

$1$ .

$- 5, 6$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 5) (x + 6)}{x - 5}$

Step 2

Cancel the common factor of

$x - 5$ .

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Step 2.1

Cancel the common factor.

$\frac{(x - 5) (x + 6)}{x - 5}$

Step 2.2

Divide

$x + 6$ by

$1$ .

$x + 6$

$\frac{x^{2} + x - 30}{x - 5}$

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