Factor 15x^2+17x+2

$15 x^{2} + 17 x + 2$

Step 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 $a \cdot c = 15 \cdot 2 = 30$ and whose sum is $b = 17$ .

Factor $17$ out of $17 x$ .

$15 x^{2} + 17 (x) + 2$

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

$15 x^{2} + (2 + 15) x + 2$

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 x^{2} + 2 x) + 15 x + 2$

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

$x (15 x + 2) + 1 (15 x + 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $15 x + 2$ .

$(15 x + 2) (x + 1)$

Factor 15x^2+17x+2

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