Algebra Examples

2 x^{2} + x - 1

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

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 - 1 = - 2

$a \cdot c = 2 \cdot - 1 = - 2$ and whose sum is

b = 1

$b = 1$ .

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Step 1.1

Multiply by

1

$1$ .

2 x^{2} + 1 x - 1

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

Step 1.2

Rewrite

1

$1$ as

- 1

$- 1$ plus

2

$2$

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

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

Step 1.3

Apply the distributive property.

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

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

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

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

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) + 2 x - 1

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

Step 2.2

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

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

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

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor,

2 x - 1

$2 x - 1$ .

(2 x - 1) (x + 1)

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

2 x^{2} + x - 1

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

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