Pre-Algebra Examples

$10 w^{6} + 34 w^{5} + 12 w^{4}$

Step 1

Factor $2 w^{4}$ out of $10 w^{6} + 34 w^{5} + 12 w^{4}$ .

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Step 1.1

Factor $2 w^{4}$ out of $10 w^{6}$ .

$2 w^{4} (5 w^{2}) + 34 w^{5} + 12 w^{4}$

Step 1.2

Factor $2 w^{4}$ out of $34 w^{5}$ .

$2 w^{4} (5 w^{2}) + 2 w^{4} (17 w) + 12 w^{4}$

Step 1.3

Factor $2 w^{4}$ out of $12 w^{4}$ .

$2 w^{4} (5 w^{2}) + 2 w^{4} (17 w) + 2 w^{4} (6)$

Step 1.4

Factor $2 w^{4}$ out of $2 w^{4} (5 w^{2}) + 2 w^{4} (17 w)$ .

$2 w^{4} (5 w^{2} + 17 w) + 2 w^{4} (6)$

Step 1.5

Factor $2 w^{4}$ out of $2 w^{4} (5 w^{2} + 17 w) + 2 w^{4} (6)$ .

$2 w^{4} (5 w^{2} + 17 w + 6)$

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 $a \cdot c = 5 \cdot 6 = 30$ and whose sum is $b = 17$ .

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Step 2.1.1.1

Factor $17$ out of $17 w$ .

$2 w^{4} (5 w^{2} + 17 (w) + 6)$

Step 2.1.1.2

Rewrite $17$ as $2$ plus $15$

$2 w^{4} (5 w^{2} + (2 + 15) w + 6)$

Step 2.1.1.3

Apply the distributive property.

$2 w^{4} (5 w^{2} + 2 w + 15 w + 6)$

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.

$2 w^{4} ((5 w^{2} + 2 w) + 15 w + 6)$

Step 2.1.2.2

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

$2 w^{4} (w (5 w + 2) + 3 (5 w + 2))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $5 w + 2$ .

$2 w^{4} ((5 w + 2) (w + 3))$

Step 2.2

Remove unnecessary parentheses.

$2 w^{4} (5 w + 2) (w + 3)$