Precalculus Examples

Given that $f (x) = x^{2} + 8 x - 20$ and $g (x) = x - 2$ ; find $f (x) \div g (x)$ and express the result in standard form.

Step 1

Remove parentheses.

$x^{2} + 8 x - 20$

Step 2

Remove parentheses.

$x - 2$

Step 3

Rewrite $f (x) \div g (x)$ .

$\frac{x^{2} + 8 x - 20}{x - 2}$

Step 4

Simplify $\frac{x^{2} + 8 x - 20}{x - 2}$ .

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Step 4.1

Factor $x^{2} + 8 x - 20$ using the AC method.

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Step 4.1.1

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 $- 20$ and whose sum is $8$ .

$- 2, 10$

Step 4.1.2

Write the factored form using these integers.

$\frac{(x - 2) (x + 10)}{x - 2}$

Step 4.2

Cancel the common factor of $x - 2$ .

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Step 4.2.1

Cancel the common factor.

$\frac{(x - 2) (x + 10)}{x - 2}$

Step 4.2.2

Divide $x + 10$ by $1$ .

$x + 10$