Factor 2x^2+x-1=0

$2 x^{2} + x - 1 = 0$

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

Multiply by $1$ .

$2 x^{2} + 1 x - 1 = 0$

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

$2 x^{2} + (- 1 + 2) x - 1 = 0$

Apply the distributive property.

$2 x^{2} - 1 x + 2 x - 1 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 1 x) + 2 x - 1 = 0$

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

$x (2 x - 1) + 1 (2 x - 1) = 0$

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

$(2 x - 1) (x + 1) = 0$

Factor 2x^2+x-1=0

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