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

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

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

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

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} - 1 x) + 6 x - 3

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

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)

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