Algebra Examples

$f (x) = \frac{3 x^{2} + 8 x}{x^{2} + 3 x - 10}$

Step 1

Factor $x$ out of $3 x^{2} + 8 x$ .

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Step 1.1

Factor $x$ out of $3 x^{2}$ .

$f (x) = \frac{x (3 x) + 8 x}{x^{2} + 3 x - 10}$

Step 1.2

Factor $x$ out of $8 x$ .

$f (x) = \frac{x (3 x) + x \cdot 8}{x^{2} + 3 x - 10}$

Step 1.3

Factor $x$ out of $x (3 x) + x \cdot 8$ .

$f (x) = \frac{x (3 x + 8)}{x^{2} + 3 x - 10}$

Step 2

Factor $x^{2} + 3 x - 10$ using the AC method.

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Step 2.1

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 $- 10$ and whose sum is $3$ .

$- 2, 5$

Step 2.2

Write the factored form using these integers.

$f (x) = \frac{x (3 x + 8)}{(x - 2) (x + 5)}$

Step 3

Since no factors can be removed from the denominator, there are no holes in the graph.

No holes

Step 4