Algebra Examples

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

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

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

$b = 1$ .

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Step 1.1

Multiply by

$1$ .

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

Step 1.2

Rewrite

$1$ as

$- 3$ plus

$4$

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

Step 1.3

Apply the distributive property.

$2 x^{2} - 3 x + 4 x - 6$

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.

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

Step 2.2

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor,

$2 x - 3$ .

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