Factor 3y^2+14y-24

$3 y^{2} + 14 y - 24$

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 $a \cdot c = 3 \cdot - 24 = - 72$ and whose sum is $b = 14$ .

Factor $14$ out of $14 y$ .

$3 y^{2} + 14 (y) - 24$

Rewrite $14$ as $- 4$ plus $18$

$3 y^{2} + (- 4 + 18) y - 24$

Apply the distributive property.

$3 y^{2} - 4 y + 18 y - 24$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 y^{2} - 4 y) + 18 y - 24$

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

$y (3 y - 4) + 6 (3 y - 4)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 y - 4$ .

$(3 y - 4) (y + 6)$

Factor 3y^2+14y-24

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