Finite Math Examples

$9 m^{3} - 51 m^{2} - 18 m$

Step 1

Factor $3 m$ out of $9 m^{3} - 51 m^{2} - 18 m$ .

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Step 1.1

Factor $3 m$ out of $9 m^{3}$ .

$3 m (3 m^{2}) - 51 m^{2} - 18 m$

Step 1.2

Factor $3 m$ out of $- 51 m^{2}$ .

$3 m (3 m^{2}) + 3 m (- 17 m) - 18 m$

Step 1.3

Factor $3 m$ out of $- 18 m$ .

$3 m (3 m^{2}) + 3 m (- 17 m) + 3 m (- 6)$

Step 1.4

Factor $3 m$ out of $3 m (3 m^{2}) + 3 m (- 17 m)$ .

$3 m (3 m^{2} - 17 m) + 3 m (- 6)$

Step 1.5

Factor $3 m$ out of $3 m (3 m^{2} - 17 m) + 3 m (- 6)$ .

$3 m (3 m^{2} - 17 m - 6)$

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 6 = - 18$ and whose sum is $b = - 17$ .

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Step 2.1.1.1

Factor $- 17$ out of $- 17 m$ .

$3 m (3 m^{2} - 17 (m) - 6)$

Step 2.1.1.2

Rewrite $- 17$ as $1$ plus $- 18$

$3 m (3 m^{2} + (1 - 18) m - 6)$

Step 2.1.1.3

Apply the distributive property.

$3 m (3 m^{2} + 1 m - 18 m - 6)$

Step 2.1.1.4

Multiply $m$ by $1$ .

$3 m (3 m^{2} + m - 18 m - 6)$

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

$3 m ((3 m^{2} + m) - 18 m - 6)$

Step 2.1.2.2

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

$3 m (m (3 m + 1) - 6 (3 m + 1))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $3 m + 1$ .

$3 m ((3 m + 1) (m - 6))$

Step 2.2

Remove unnecessary parentheses.

$3 m (3 m + 1) (m - 6)$