Factor 30x^2+25x+5

$30 x^{2} + 25 x + 5$

Step 1

Factor $5$ out of $30 x^{2} + 25 x + 5$ .

Factor $5$ out of $30 x^{2}$ .

$5 (6 x^{2}) + 25 x + 5$

Factor $5$ out of $25 x$ .

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

Factor $5$ out of $5$ .

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

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

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

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

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

Step 2

Factor.

Factor by grouping.

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

Factor $5$ out of $5 x$ .

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

Rewrite $5$ as $2$ plus $3$

$5 (6 x^{2} + (2 + 3) x + 1)$

Apply the distributive property.

$5 (6 x^{2} + 2 x + 3 x + 1)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$5 ((6 x^{2} + 2 x) + 3 x + 1)$

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

$5 (2 x (3 x + 1) + 1 (3 x + 1))$

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

$5 ((3 x + 1) (2 x + 1))$

Remove unnecessary parentheses.

$5 (3 x + 1) (2 x + 1)$

Factor 30x^2+25x+5

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