Algebra Examples

$6 x^{2} + 5 x - 6$

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 $a \cdot c = 6 \cdot - 6 = - 36$ and whose sum is $b = 5$ .

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Step 1.1

Factor $5$ out of $5 x$ .

$6 x^{2} + 5 (x) - 6$

Step 1.2

Rewrite $5$ as $- 4$ plus $9$

$6 x^{2} + (- 4 + 9) x - 6$

Step 1.3

Apply the distributive property.

$6 x^{2} - 4 x + 9 x - 6$

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.

$(6 x^{2} - 4 x) + 9 x - 6$

Step 2.2

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

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

Step 3

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

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