Factor 6t^2+7t-5

$6 t^{2} + 7 t - 5$

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 $a \cdot c = 6 \cdot - 5 = - 30$ and whose sum is $b = 7$ .

Factor $7$ out of $7 t$ .

$6 t^{2} + 7 (t) - 5$

Rewrite $7$ as $- 3$ plus $10$

$6 t^{2} + (- 3 + 10) t - 5$

Apply the distributive property.

$6 t^{2} - 3 t + 10 t - 5$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 t^{2} - 3 t) + 10 t - 5$

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

$3 t (2 t - 1) + 5 (2 t - 1)$

Factor the polynomial by factoring out the greatest common factor, $2 t - 1$ .

$(2 t - 1) (3 t + 5)$

Factor 6t^2+7t-5

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