Pre-Algebra Examples

$10 x^{3} + 12 x^{2} + 2 x$

Step 1

Factor $2 x$ out of $10 x^{3} + 12 x^{2} + 2 x$ .

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Step 1.1

Factor $2 x$ out of $10 x^{3}$ .

$2 x (5 x^{2}) + 12 x^{2} + 2 x$

Step 1.2

Factor $2 x$ out of $12 x^{2}$ .

$2 x (5 x^{2}) + 2 x (6 x) + 2 x$

Step 1.3

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

$2 x (5 x^{2}) + 2 x (6 x) + 2 x (1)$

Step 1.4

Factor $2 x$ out of $2 x (5 x^{2}) + 2 x (6 x)$ .

$2 x (5 x^{2} + 6 x) + 2 x (1)$

Step 1.5

Factor $2 x$ out of $2 x (5 x^{2} + 6 x) + 2 x (1)$ .

$2 x (5 x^{2} + 6 x + 1)$

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 $a \cdot c = 5 \cdot 1 = 5$ and whose sum is $b = 6$ .

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Step 2.1.1.1

Factor $6$ out of $6 x$ .

$2 x (5 x^{2} + 6 (x) + 1)$

Step 2.1.1.2

Rewrite $6$ as $1$ plus $5$

$2 x (5 x^{2} + (1 + 5) x + 1)$

Step 2.1.1.3

Apply the distributive property.

$2 x (5 x^{2} + 1 x + 5 x + 1)$

Step 2.1.1.4

Multiply $x$ by $1$ .

$2 x (5 x^{2} + x + 5 x + 1)$

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.

$2 x ((5 x^{2} + x) + 5 x + 1)$

Step 2.1.2.2

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

$2 x (x (5 x + 1) + 1 (5 x + 1))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $5 x + 1$ .

$2 x ((5 x + 1) (x + 1))$

Step 2.2

Remove unnecessary parentheses.

$2 x (5 x + 1) (x + 1)$