Factor 10x^2-3x-1

$10 x^{2} - 3 x - 1$

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

Factor $- 3$ out of $- 3 x$ .

$10 x^{2} - 3 (x) - 1$

Rewrite $- 3$ as $2$ plus $- 5$

$10 x^{2} + (2 - 5) x - 1$

Apply the distributive property.

$10 x^{2} + 2 x - 5 x - 1$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(10 x^{2} + 2 x) - 5 x - 1$

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

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

Step 3

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

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

Factor 10x^2-3x-1

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