Factor f(x)=6x^2+x-2

$f (x) = 6 x^{2} + x - 2$

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 $a \cdot c = 6 \cdot - 2 = - 12$ and whose sum is $b = 1$ .

Multiply by $1$ .

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

Rewrite $1$ as $- 3$ plus $4$

$f (x) = 6 x^{2} + (- 3 + 4) x - 2$

Apply the distributive property.

$f (x) = 6 x^{2} - 3 x + 4 x - 2$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$f (x) = (6 x^{2} - 3 x) + 4 x - 2$

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

$f (x) = 3 x (2 x - 1) + 2 (2 x - 1)$

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

$f (x) = (2 x - 1) (3 x + 2)$

Factor f(x)=6x^2+x-2

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