Factor 3y^2+29y-10

$3 y^{2} + 29 y - 10$

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 $b = 29$ .

Factor $29$ out of $29 y$ .

$3 y^{2} + 29 (y) - 10$

Rewrite $29$ as $- 1$ plus $30$

$3 y^{2} + (- 1 + 30) y - 10$

Apply the distributive property.

$3 y^{2} - 1 y + 30 y - 10$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 y^{2} - 1 y) + 30 y - 10$

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

$y (3 y - 1) + 10 (3 y - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 y - 1$ .

$(3 y - 1) (y + 10)$

Factor 3y^2+29y-10

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