Factor 30x^2-x-14

$30 x^{2} - x - 14$

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 $a \cdot c = 30 \cdot - 14 = - 420$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- x$ .

$30 x^{2} - (x) - 14$

Rewrite $- 1$ as $20$ plus $- 21$

$30 x^{2} + (20 - 21) x - 14$

Apply the distributive property.

$30 x^{2} + 20 x - 21 x - 14$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(30 x^{2} + 20 x) - 21 x - 14$

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

$10 x (3 x + 2) - 7 (3 x + 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x + 2$ .

$(3 x + 2) (10 x - 7)$

Factor 30x^2-x-14

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