Factor 5x^2+14x-3

$5 x^{2} + 14 x - 3$

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 $a \cdot c = 5 \cdot - 3 = - 15$ and whose sum is $b = 14$ .

Factor $14$ out of $14 x$ .

$5 x^{2} + 14 (x) - 3$

Rewrite $14$ as $- 1$ plus $15$

$5 x^{2} + (- 1 + 15) x - 3$

Apply the distributive property.

$5 x^{2} - 1 x + 15 x - 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} - 1 x) + 15 x - 3$

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

$x (5 x - 1) + 3 (5 x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x - 1$ .

$(5 x - 1) (x + 3)$

Factor 5x^2+14x-3

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