Precalculus Examples

Given that $f (x) = x^{2} - 13 x + 40$ and $g (x) = x - 5$ ; find $f (x) \div g (x)$ and express the result in standard form.

Step 1

Remove parentheses.

$x^{2} - 13 x + 40$

Step 2

Remove parentheses.

$x - 5$

Step 3

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

$\frac{x^{2} - 13 x + 40}{x - 5}$

Step 4

Simplify $\frac{x^{2} - 13 x + 40}{x - 5}$ .

Tap for more steps...

Step 4.1

Factor $x^{2} - 13 x + 40$ using the AC method.

Tap for more steps...

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 $40$ and whose sum is $- 13$ .

$- 8, - 5$

Step 4.1.2

Write the factored form using these integers.

$\frac{(x - 8) (x - 5)}{x - 5}$

Step 4.2

Cancel the common factor of $x - 5$ .

Tap for more steps...

Step 4.2.1

Cancel the common factor.

$\frac{(x - 8) (x - 5)}{x - 5}$

Step 4.2.2

Divide $x - 8$ by $1$ .

$x - 8$