Precalculus Examples

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

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

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Step 1.1

Factor $- 1$ out of $- x$ .

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

Step 1.2

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

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

Step 1.3

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

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

Step 2.2

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

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

Step 3

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

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