Factor 3x^2+2x-1

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

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 $a \cdot c = 3 \cdot - 1 = - 3$ and whose sum is $b = 2$ .

Factor $2$ out of $2 x$ .

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

Rewrite $2$ as $- 1$ plus $3$

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x - 1$ .

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

Factor 3x^2+2x-1

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