Finite Math Examples

$p (x) = 2 x^{3} - 3 x^{2} - 2 x$

Step 1

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

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Step 1.1

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

$p (x) = x (2 x^{2}) - 3 x^{2} - 2 x$

Step 1.2

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

$p (x) = x (2 x^{2}) + x (- 3 x) - 2 x$

Step 1.3

Factor $x$ out of $- 2 x$ .

$p (x) = x (2 x^{2}) + x (- 3 x) + x \cdot - 2$

Step 1.4

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

$p (x) = x (2 x^{2} - 3 x) + x \cdot - 2$

Step 1.5

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

$p (x) = x (2 x^{2} - 3 x - 2)$

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 $a \cdot c = 2 \cdot - 2 = - 4$ and whose sum is $b = - 3$ .

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Step 2.1.1.1

Factor $- 3$ out of $- 3 x$ .

$p (x) = x (2 x^{2} - 3 x - 2)$

Step 2.1.1.2

Rewrite $- 3$ as $1$ plus $- 4$

$p (x) = x (2 x^{2} + (1 - 4) x - 2)$

Step 2.1.1.3

Apply the distributive property.

$p (x) = x (2 x^{2} + 1 x - 4 x - 2)$

Step 2.1.1.4

Multiply $x$ by $1$ .

$p (x) = x (2 x^{2} + x - 4 x - 2)$

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.

$p (x) = x ((2 x^{2} + x) - 4 x - 2)$

Step 2.1.2.2

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

$p (x) = x (x (2 x + 1) - 2 (2 x + 1))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$p (x) = x ((2 x + 1) (x - 2))$

Step 2.2

Remove unnecessary parentheses.

$p (x) = x (2 x + 1) (x - 2)$