Factor 7x^2+6x-1

$7 x^{2} + 6 x - 1$

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 $a \cdot c = 7 \cdot - 1 = - 7$ and whose sum is $b = 6$ .

Factor $6$ out of $6 x$ .

$7 x^{2} + 6 (x) - 1$

Rewrite $6$ as $- 1$ plus $7$

$7 x^{2} + (- 1 + 7) x - 1$

Apply the distributive property.

$7 x^{2} - 1 x + 7 x - 1$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} - 1 x) + 7 x - 1$

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

$x (7 x - 1) + 1 (7 x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x - 1$ .

$(7 x - 1) (x + 1)$

Factor 7x^2+6x-1

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