Factor 3x^2+x-2=0

$3 x^{2} + x - 2 = 0$

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 $a \cdot c = 3 \cdot - 2 = - 6$ and whose sum is $b = 1$ .

Multiply by $1$ .

$3 x^{2} + 1 x - 2 = 0$

Rewrite $1$ as $- 2$ plus $3$

$3 x^{2} + (- 2 + 3) x - 2 = 0$

Apply the distributive property.

$3 x^{2} - 2 x + 3 x - 2 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} - 2 x) + 3 x - 2 = 0$

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

$x (3 x - 2) + 1 (3 x - 2) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 x - 2$ .

$(3 x - 2) (x + 1) = 0$

Factor 3x^2+x-2=0

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