Factor 24x^2+42x+15

$24 x^{2} + 42 x + 15$

Step 1

Factor $3$ out of $24 x^{2} + 42 x + 15$ .

Factor $3$ out of $24 x^{2}$ .

$3 (8 x^{2}) + 42 x + 15$

Factor $3$ out of $42 x$ .

$3 (8 x^{2}) + 3 (14 x) + 15$

Factor $3$ out of $15$ .

$3 (8 x^{2}) + 3 (14 x) + 3 (5)$

Factor $3$ out of $3 (8 x^{2}) + 3 (14 x)$ .

$3 (8 x^{2} + 14 x) + 3 (5)$

Factor $3$ out of $3 (8 x^{2} + 14 x) + 3 (5)$ .

$3 (8 x^{2} + 14 x + 5)$

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 $a \cdot c = 8 \cdot 5 = 40$ and whose sum is $b = 14$ .

Factor $14$ out of $14 x$ .

$3 (8 x^{2} + 14 (x) + 5)$

Rewrite $14$ as $4$ plus $10$

$3 (8 x^{2} + (4 + 10) x + 5)$

Apply the distributive property.

$3 (8 x^{2} + 4 x + 10 x + 5)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((8 x^{2} + 4 x) + 10 x + 5)$

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

$3 (4 x (2 x + 1) + 5 (2 x + 1))$

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

$3 ((2 x + 1) (4 x + 5))$

Remove unnecessary parentheses.

$3 (2 x + 1) (4 x + 5)$

Factor 24x^2+42x+15

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