Factor 2t^2+5t-12

$2 t^{2} + 5 t - 12$

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 $a \cdot c = 2 \cdot - 12 = - 24$ and whose sum is $b = 5$ .

Factor $5$ out of $5 t$ .

$2 t^{2} + 5 (t) - 12$

Rewrite $5$ as $- 3$ plus $8$

$2 t^{2} + (- 3 + 8) t - 12$

Apply the distributive property.

$2 t^{2} - 3 t + 8 t - 12$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 t^{2} - 3 t) + 8 t - 12$

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

$t (2 t - 3) + 4 (2 t - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 t - 3$ .

$(2 t - 3) (t + 4)$

Factor 2t^2+5t-12

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