Factor 8x^2+2x-1

$8 x^{2} + 2 x - 1$

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 $a \cdot c = 8 \cdot - 1 = - 8$ and whose sum is $b = 2$ .

Factor $2$ out of $2 x$ .

$8 x^{2} + 2 (x) - 1$

Rewrite $2$ as $- 2$ plus $4$

$8 x^{2} + (- 2 + 4) x - 1$

Apply the distributive property.

$8 x^{2} - 2 x + 4 x - 1$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 x^{2} - 2 x) + 4 x - 1$

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

$2 x (4 x - 1) + 1 (4 x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x - 1$ .

$(4 x - 1) (2 x + 1)$

Factor 8x^2+2x-1

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