Algebra Examples

2 x^{2} - 5 x - 3

$2 x^{2} - 5 x - 3$

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 - 3 = - 6

$a \cdot c = 2 \cdot - 3 = - 6$ 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) - 3

$2 x^{2} - 5 (x) - 3$

Step 1.2

Rewrite

- 5

$- 5$ as

1

$1$ plus

- 6

$- 6$

2 x^{2} + (1 - 6) x - 3

$2 x^{2} + (1 - 6) x - 3$

Step 1.3

Apply the distributive property.

2 x^{2} + 1 x - 6 x - 3

$2 x^{2} + 1 x - 6 x - 3$

Step 1.4

Multiply

x

$x$ by

1

$1$ .

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

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

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

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

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) - 6 x - 3

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

Step 2.2

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

x (2 x + 1) - 3 (2 x + 1)

$x (2 x + 1) - 3 (2 x + 1)$

x (2 x + 1) - 3 (2 x + 1)

$x (2 x + 1) - 3 (2 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

2 x + 1

$2 x + 1$ .

(2 x + 1) (x - 3)

$(2 x + 1) (x - 3)$

2 x^{2} - 5 x - 3

$2 x^{2} - 5 x - 3$

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