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.

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

Multiply $x$ by $1$ .

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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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