Factor 3y^2+17y+10

$3 y^{2} + 17 y + 10$

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 $a \cdot c = 3 \cdot 10 = 30$ and whose sum is $b = 17$ .

Factor $17$ out of $17 y$ .

$3 y^{2} + 17 (y) + 10$

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

$3 y^{2} + (2 + 15) y + 10$

Apply the distributive property.

$3 y^{2} + 2 y + 15 y + 10$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 y^{2} + 2 y) + 15 y + 10$

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

$y (3 y + 2) + 5 (3 y + 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 y + 2$ .

$(3 y + 2) (y + 5)$

Factor 3y^2+17y+10

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