Factor 14x^2+x-3

$14 x^{2} + x - 3$

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 $a \cdot c = 14 \cdot - 3 = - 42$ and whose sum is $b = 1$ .

Multiply by $1$ .

$14 x^{2} + 1 x - 3$

Rewrite $1$ as $- 6$ plus $7$

$14 x^{2} + (- 6 + 7) x - 3$

Apply the distributive property.

$14 x^{2} - 6 x + 7 x - 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(14 x^{2} - 6 x) + 7 x - 3$

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

$2 x (7 x - 3) + 1 (7 x - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x - 3$ .

$(7 x - 3) (2 x + 1)$

Factor 14x^2+x-3

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