Algebra Examples

6 x^{2} + 5 x - 6

$6 x^{2} + 5 x - 6$

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 = 6 \cdot - 6 = - 36

$a \cdot c = 6 \cdot - 6 = - 36$ and whose sum is

b = 5

$b = 5$ .

Tap for more steps...

Step 1.1

Factor

5

$5$ out of

5 x

$5 x$ .

6 x^{2} + 5 (x) - 6

$6 x^{2} + 5 (x) - 6$

Step 1.2

Rewrite

5

$5$ as

- 4

$- 4$ plus

9

$9$

6 x^{2} + (- 4 + 9) x - 6

$6 x^{2} + (- 4 + 9) x - 6$

Step 1.3

Apply the distributive property.

6 x^{2} - 4 x + 9 x - 6

$6 x^{2} - 4 x + 9 x - 6$

6 x^{2} - 4 x + 9 x - 6

$6 x^{2} - 4 x + 9 x - 6$

Step 2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.1

Group the first two terms and the last two terms.

(6 x^{2} - 4 x) + 9 x - 6

$(6 x^{2} - 4 x) + 9 x - 6$

Step 2.2

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

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

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

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor,

3 x - 2

$3 x - 2$ .

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

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

6 x^{2} + 5 x - 6

$6 x^{2} + 5 x - 6$

(

)

[

]

√



≥

















≤















∩

∪







∞











