Finite Math Examples

$\frac{x^{3} + 10 x^{2}}{x^{2} + 5 x - 50}$

Step 1

Factor $x^{2}$ out of $x^{3} + 10 x^{2}$ .

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Step 1.1

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

$\frac{x^{2} x + 10 x^{2}}{x^{2} + 5 x - 50}$

Step 1.2

Factor $x^{2}$ out of $10 x^{2}$ .

$\frac{x^{2} x + x^{2} \cdot 10}{x^{2} + 5 x - 50}$

Step 1.3

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot 10$ .

$\frac{x^{2} (x + 10)}{x^{2} + 5 x - 50}$

Step 2

Factor $x^{2} + 5 x - 50$ 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 $- 50$ and whose sum is $5$ .

$- 5, 10$

Step 2.2

Write the factored form using these integers.

$\frac{x^{2} (x + 10)}{(x - 5) (x + 10)}$

Step 3

Cancel the common factor of $x + 10$ .

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Step 3.1

Cancel the common factor.

$\frac{x^{2} (x + 10)}{(x - 5) (x + 10)}$

Step 3.2

Rewrite the expression.

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