Pre-Algebra Examples

$5 r^{3} + 15 r^{2} - 125 r - 375$

Step 1

Factor $5$ out of $5 r^{3} + 15 r^{2} - 125 r - 375$ .

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Step 1.1

Factor $5$ out of $5 r^{3}$ .

$5 (r^{3}) + 15 r^{2} - 125 r - 375$

Step 1.2

Factor $5$ out of $15 r^{2}$ .

$5 (r^{3}) + 5 (3 r^{2}) - 125 r - 375$

Step 1.3

Factor $5$ out of $- 125 r$ .

$5 (r^{3}) + 5 (3 r^{2}) + 5 (- 25 r) - 375$

Step 1.4

Factor $5$ out of $- 375$ .

$5 r^{3} + 5 (3 r^{2}) + 5 (- 25 r) + 5 \cdot - 75$

Step 1.5

Factor $5$ out of $5 r^{3} + 5 (3 r^{2})$ .

$5 (r^{3} + 3 r^{2}) + 5 (- 25 r) + 5 \cdot - 75$

Step 1.6

Factor $5$ out of $5 (r^{3} + 3 r^{2}) + 5 (- 25 r)$ .

$5 (r^{3} + 3 r^{2} - 25 r) + 5 \cdot - 75$

Step 1.7

Factor $5$ out of $5 (r^{3} + 3 r^{2} - 25 r) + 5 \cdot - 75$ .

$5 (r^{3} + 3 r^{2} - 25 r - 75)$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$5 ((r^{3} + 3 r^{2}) - 25 r - 75)$

Step 2.2

Factor out the greatest common factor (GCF) from each group.

$5 (r^{2} (r + 3) - 25 (r + 3))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $r + 3$ .

$5 ((r + 3) (r^{2} - 25))$

Step 4

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

$5 ((r + 3) (r^{2} - 5^{2}))$

Step 5

Factor.

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Step 5.1

Factor.

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Step 5.1.1

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

$5 ((r + 3) ((r + 5) (r - 5)))$

Step 5.1.2

Remove unnecessary parentheses.

$5 ((r + 3) (r + 5) (r - 5))$

Step 5.2

Remove unnecessary parentheses.

$5 (r + 3) (r + 5) (r - 5)$