Factor 5t^2+17t-12

$5 t^{2} + 17 t - 12$

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 $a \cdot c = 5 \cdot - 12 = - 60$ and whose sum is $b = 17$ .

Factor $17$ out of $17 t$ .

$5 t^{2} + 17 (t) - 12$

Rewrite $17$ as $- 3$ plus $20$

$5 t^{2} + (- 3 + 20) t - 12$

Apply the distributive property.

$5 t^{2} - 3 t + 20 t - 12$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 t^{2} - 3 t) + 20 t - 12$

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

$t (5 t - 3) + 4 (5 t - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 t - 3$ .

$(5 t - 3) (t + 4)$

Factor 5t^2+17t-12

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