Algebra Examples

$6 x^{2} - x - 15$

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

$a \cdot c = 6 \cdot - 15 = - 90$ and whose sum is

$b = - 1$ .

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Step 1.1

Factor

$- 1$ out of

$- x$ .

$6 x^{2} - (x) - 15$

Step 1.2

Rewrite

$- 1$ as

$9$ plus

$- 10$

$6 x^{2} + (9 - 10) x - 15$

Step 1.3

Apply the distributive property.

$6 x^{2} + 9 x - 10 x - 15$

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.

$(6 x^{2} + 9 x) - 10 x - 15$

Step 2.2

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

$3 x (2 x + 3) - 5 (2 x + 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

$2 x + 3$ .

$(2 x + 3) (3 x - 5)$