Precalculus Examples

$x^{3} + 5 x^{2} - 25 x - 125$

Step 1

Factor out the greatest common factor from each group.

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Step 1.1

Group the first two terms and the last two terms.

$(x^{3} + 5 x^{2}) - 25 x - 125$

Step 1.2

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

$x^{2} (x + 5) - 25 (x + 5)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $x + 5$ .

$(x + 5) (x^{2} - 25)$

Step 3

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

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

Step 4

Factor.

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Step 4.1

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 $b = 5$ .

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

Step 4.2

Remove unnecessary parentheses.

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

Step 5

Combine exponents.

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Step 5.1

Raise $x + 5$ to the power of $1$ .

${(x + 5)}^{1} (x + 5) (x - 5)$

Step 5.2

Raise $x + 5$ to the power of $1$ .

${(x + 5)}^{1} {(x + 5)}^{1} (x - 5)$

Step 5.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(x + 5)}^{1 + 1} (x - 5)$

Step 5.4

Add $1$ and $1$ .

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