Algebra Examples

2 x^{2} - 3 x - 20

$2 x^{2} - 3 x - 20$

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 - 20 = - 40

$a \cdot c = 2 \cdot - 20 = - 40$ and whose sum is

b = - 3

$b = - 3$ .

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Step 1.1

Factor

- 3

$- 3$ out of

- 3 x

$- 3 x$ .

2 x^{2} - 3 (x) - 20

$2 x^{2} - 3 (x) - 20$

Step 1.2

Rewrite

- 3

$- 3$ as

5

$5$ plus

- 8

$- 8$

2 x^{2} + (5 - 8) x - 20

$2 x^{2} + (5 - 8) x - 20$

Step 1.3

Apply the distributive property.

2 x^{2} + 5 x - 8 x - 20

$2 x^{2} + 5 x - 8 x - 20$

2 x^{2} + 5 x - 8 x - 20

$2 x^{2} + 5 x - 8 x - 20$

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) - 8 x - 20

$(2 x^{2} + 5 x) - 8 x - 20$

Step 2.2

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

x (2 x + 5) - 4 (2 x + 5)

$x (2 x + 5) - 4 (2 x + 5)$

x (2 x + 5) - 4 (2 x + 5)

$x (2 x + 5) - 4 (2 x + 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

2 x + 5

$2 x + 5$ .

(2 x + 5) (x - 4)

$(2 x + 5) (x - 4)$