Pre-Algebra Examples

$w^{3} - 3 w^{2} - 18 w$

Step 1

Factor out the GCF of $w$ from $w^{3} - 3 w^{2} - 18 w$ .

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Step 1.1

Factor out the GCF of $w$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $w$ from the expression $w^{3}$ .

$w (w^{2}) - 3 w^{2} - 18 w$

Step 1.1.2

Factor out the GCF of $w$ from the expression $- 3 w^{2}$ .

$w (w^{2}) + w (- 3 w) - 18 w$

Step 1.1.3

Factor out the GCF of $w$ from the expression $- 18 w$ .

$w (w^{2}) + w (- 3 w) + w (- 18)$

Step 1.2

Since all the terms share a common factor of $w$ , it can be factored out of each term.

$w (w^{2} - 3 w - 18)$

Step 2

Factor $w^{2} - 3 w - 18$ 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 $- 18$ and whose sum is $- 3$ .

$- 6, 3$

Step 2.2

Write the factored form using these integers.

$w ((w - 6) (w + 3))$