Algebra Examples

2 x^{2} + 9 x + 4

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

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 4 = 8

$a \cdot c = 2 \cdot 4 = 8$ and whose sum is

b = 9

$b = 9$ .

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Step 1.1

Factor

9

$9$ out of

9 x

$9 x$ .

2 x^{2} + 9 (x) + 4

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

Step 1.2

Rewrite

9

$9$ as

1

$1$ plus

8

$8$

2 x^{2} + (1 + 8) x + 4

$2 x^{2} + (1 + 8) x + 4$

Step 1.3

Apply the distributive property.

2 x^{2} + 1 x + 8 x + 4

$2 x^{2} + 1 x + 8 x + 4$

Step 1.4

Multiply

x

$x$ by

1

$1$ .

2 x^{2} + x + 8 x + 4

$2 x^{2} + x + 8 x + 4$

2 x^{2} + x + 8 x + 4

$2 x^{2} + x + 8 x + 4$

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} + x) + 8 x + 4

$(2 x^{2} + x) + 8 x + 4$

Step 2.2

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

x (2 x + 1) + 4 (2 x + 1)

$x (2 x + 1) + 4 (2 x + 1)$

x (2 x + 1) + 4 (2 x + 1)

$x (2 x + 1) + 4 (2 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

2 x + 1

$2 x + 1$ .

(2 x + 1) (x + 4)

$(2 x + 1) (x + 4)$