Factor 2x^2-x-1

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

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

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

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

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

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

Apply the distributive property.

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

Multiply $x$ by $1$ .

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

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

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

Factor 2x^2-x-1

Related Questions

Support LCMGCF.com by disabling your adblocker.