Algebra Examples

Factor the polynomial $3 x^{2} - 75$

Step 1

Factor $3$ out of $3 x^{2} - 75$ .

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Step 1.1

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

$3 (x^{2}) - 75$

Step 1.2

Factor $3$ out of $- 75$ .

$3 x^{2} + 3 \cdot - 25$

Step 1.3

Factor $3$ out of $3 x^{2} + 3 \cdot - 25$ .

$3 (x^{2} - 25)$

Step 2

Rewrite $25$ as $5^{2}$ .

$3 (x^{2} - 5^{2})$

Step 3

Factor.

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Step 3.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$3 ((x + 5) (x - 5))$

Step 3.2

Remove unnecessary parentheses.

$3 (x + 5) (x - 5)$