Factor 12x^2-25x-7

$12 x^{2} - 25 x - 7$

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 $a \cdot c = 12 \cdot - 7 = - 84$ and whose sum is $b = - 25$ .

Factor $- 25$ out of $- 25 x$ .

$12 x^{2} - 25 (x) - 7$

Rewrite $- 25$ as $3$ plus $- 28$

$12 x^{2} + (3 - 28) x - 7$

Apply the distributive property.

$12 x^{2} + 3 x - 28 x - 7$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 x^{2} + 3 x) - 28 x - 7$

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

$3 x (4 x + 1) - 7 (4 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x + 1$ .

$(4 x + 1) (3 x - 7)$

Factor 12x^2-25x-7

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