Algebra Examples

Factor: $2 x^{2} + 5 x - 3$

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 $b = 5$ .

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Step 1.1

Factor $5$ out of $5 x$ .

$2 x^{2} + 5 (x) - 3$

Step 1.2

Rewrite $5$ as $- 1$ plus $6$

$2 x^{2} + (- 1 + 6) x - 3$

Step 1.3

Apply the distributive property.

$2 x^{2} - 1 x + 6 x - 3$

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.

$(2 x^{2} - 1 x) + 6 x - 3$

Step 2.2

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

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

Step 3

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

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