Factor 14x^2-11x+2

$14 x^{2} - 11 x + 2$

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 $a \cdot c = 14 \cdot 2 = 28$ and whose sum is $b = - 11$ .

Factor $- 11$ out of $- 11 x$ .

$14 x^{2} - 11 (x) + 2$

Rewrite $- 11$ as $- 4$ plus $- 7$

$14 x^{2} + (- 4 - 7) x + 2$

Apply the distributive property.

$14 x^{2} - 4 x - 7 x + 2$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(14 x^{2} - 4 x) - 7 x + 2$

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

$2 x (7 x - 2) - (7 x - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x - 2$ .

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

Factor 14x^2-11x+2

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