Algebra Examples

6 x^{2} - 13 x + 6

$6 x^{2} - 13 x + 6$

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

$b = - 13$ .

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Step 1.1

Factor

$- 13$ out of

$- 13 x$ .

$6 x^{2} - 13 (x) + 6$

Step 1.2

Rewrite

$- 13$ 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,

$3 x - 2$ .

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