Factor 6x^2+11x-7

$6 x^{2} + 11 x - 7$

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 $a \cdot c = 6 \cdot - 7 = - 42$ and whose sum is $b = 11$ .

Factor $11$ out of $11 x$ .

$6 x^{2} + 11 (x) - 7$

Rewrite $11$ as $- 3$ plus $14$

$6 x^{2} + (- 3 + 14) x - 7$

Apply the distributive property.

$6 x^{2} - 3 x + 14 x - 7$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 x^{2} - 3 x) + 14 x - 7$

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

$3 x (2 x - 1) + 7 (2 x - 1)$

Step 3

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

$(2 x - 1) (3 x + 7)$

Factor 6x^2+11x-7

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