Algebra Examples

2 x^{2} - 5 x + 2

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

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 2 = 4

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

b = - 5

$b = - 5$ .

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Step 1.1

Factor

- 5

$- 5$ out of

- 5 x

$- 5 x$ .

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

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

Step 1.2

Rewrite

- 5

$- 5$ as

- 1

$- 1$ plus

- 4

$- 4$

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

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

Step 1.3

Apply the distributive property.

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

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

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

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

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} - 1 x) - 4 x + 2

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

Step 2.2

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

x (2 x - 1) - 2 (2 x - 1)

$x (2 x - 1) - 2 (2 x - 1)$

x (2 x - 1) - 2 (2 x - 1)

$x (2 x - 1) - 2 (2 x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

2 x - 1

$2 x - 1$ .

(2 x - 1) (x - 2)

$(2 x - 1) (x - 2)$

2 x^{2} - 5 x + 2

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

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