Factor 10x^2-x-3

$10 x^{2} - x - 3$

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 $a \cdot c = 10 \cdot - 3 = - 30$ and whose sum is $b = - 1$ .

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

$10 x^{2} - (x) - 3$

Rewrite $- 1$ as $5$ plus $- 6$

$10 x^{2} + (5 - 6) x - 3$

Apply the distributive property.

$10 x^{2} + 5 x - 6 x - 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(10 x^{2} + 5 x) - 6 x - 3$

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

$5 x (2 x + 1) - 3 (2 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$(2 x + 1) (5 x - 3)$

Factor 10x^2-x-3

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