Algebra Examples

$x^{3} - 3 x^{2} - 10 x$

Step 1

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

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Step 1.1

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

$x \cdot x^{2} - 3 x^{2} - 10 x$

Step 1.2

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

$x \cdot x^{2} + x (- 3 x) - 10 x$

Step 1.3

Factor $x$ out of $- 10 x$ .

$x \cdot x^{2} + x (- 3 x) + x \cdot - 10$

Step 1.4

Factor $x$ out of $x \cdot x^{2} + x (- 3 x)$ .

$x (x^{2} - 3 x) + x \cdot - 10$

Step 1.5

Factor $x$ out of $x (x^{2} - 3 x) + x \cdot - 10$ .

$x (x^{2} - 3 x - 10)$

Step 2

Factor.

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Step 2.1

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

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Step 2.1.1

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

$- 5, 2$

Step 2.1.2

Write the factored form using these integers.

$x ((x - 5) (x + 2))$

Step 2.2

Remove unnecessary parentheses.

$x (x - 5) (x + 2)$