Algebra Examples

2 x^{2} + 7 x + 6

$2 x^{2} + 7 x + 6$

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 6 = 12

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

b = 7

$b = 7$ .

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Step 1.1

Factor

7

$7$ out of

7 x

$7 x$ .

2 x^{2} + 7 (x) + 6

$2 x^{2} + 7 (x) + 6$

Step 1.2

Rewrite

7

$7$ as

3

$3$ plus

4

$4$

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

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

Step 1.3

Apply the distributive property.

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

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

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

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

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

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

Step 2.2

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

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

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

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor,

2 x + 3

$2 x + 3$ .

(2 x + 3) (x + 2)

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