Algebra Examples

2 x^{2} + 11 x + 15

$2 x^{2} + 11 x + 15$

Step 1

For a polynomial of the form

a x^{2} + b x + c

$a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is

a \cdot c = 2 \cdot 15 = 30

$a \cdot c = 2 \cdot 15 = 30$ and whose sum is

b = 11

$b = 11$ .

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Step 1.1

Factor

11

$11$ out of

11 x

$11 x$ .

2 x^{2} + 11 (x) + 15

$2 x^{2} + 11 (x) + 15$

Step 1.2

Rewrite

11

$11$ as

5

$5$ plus

6

$6$

2 x^{2} + (5 + 6) x + 15

$2 x^{2} + (5 + 6) x + 15$

Step 1.3

Apply the distributive property.

2 x^{2} + 5 x + 6 x + 15

$2 x^{2} + 5 x + 6 x + 15$

2 x^{2} + 5 x + 6 x + 15

$2 x^{2} + 5 x + 6 x + 15$

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.

(2 x^{2} + 5 x) + 6 x + 15

$(2 x^{2} + 5 x) + 6 x + 15$

Step 2.2

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

x (2 x + 5) + 3 (2 x + 5)

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

x (2 x + 5) + 3 (2 x + 5)

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

Step 3

Factor the polynomial by factoring out the greatest common factor,

2 x + 5

$2 x + 5$ .

(2 x + 5) (x + 3)

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