Factor 20x^2+40x+15

$20 x^{2} + 40 x + 15$

Step 1

Factor $5$ out of $20 x^{2} + 40 x + 15$ .

Factor $5$ out of $20 x^{2}$ .

$5 (4 x^{2}) + 40 x + 15$

Factor $5$ out of $40 x$ .

$5 (4 x^{2}) + 5 (8 x) + 15$

Factor $5$ out of $15$ .

$5 (4 x^{2}) + 5 (8 x) + 5 (3)$

Factor $5$ out of $5 (4 x^{2}) + 5 (8 x)$ .

$5 (4 x^{2} + 8 x) + 5 (3)$

Factor $5$ out of $5 (4 x^{2} + 8 x) + 5 (3)$ .

$5 (4 x^{2} + 8 x + 3)$

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 $a \cdot c = 4 \cdot 3 = 12$ and whose sum is $b = 8$ .

Factor $8$ out of $8 x$ .

$5 (4 x^{2} + 8 (x) + 3)$

Rewrite $8$ as $2$ plus $6$

$5 (4 x^{2} + (2 + 6) x + 3)$

Apply the distributive property.

$5 (4 x^{2} + 2 x + 6 x + 3)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$5 ((4 x^{2} + 2 x) + 6 x + 3)$

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

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

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

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

Remove unnecessary parentheses.

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

Factor 20x^2+40x+15

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