Factor 20x^2-3x-2

$20 x^{2} - 3 x - 2$

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 $a \cdot c = 20 \cdot - 2 = - 40$ and whose sum is $b = - 3$ .

Factor $- 3$ out of $- 3 x$ .

$20 x^{2} - 3 (x) - 2$

Rewrite $- 3$ as $5$ plus $- 8$

$20 x^{2} + (5 - 8) x - 2$

Apply the distributive property.

$20 x^{2} + 5 x - 8 x - 2$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(20 x^{2} + 5 x) - 8 x - 2$

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

$5 x (4 x + 1) - 2 (4 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x + 1$ .

$(4 x + 1) (5 x - 2)$

Factor 20x^2-3x-2

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