Algebra Examples

x^{3} - x^{2} - 2 x = 0

$x^{3} - x^{2} - 2 x = 0$

Step 1

Factor

x

$x$ out of

x^{3} - x^{2} - 2 x

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

Tap for more steps...

Step 1.1

Factor

x

$x$ out of

x^{3}

$x^{3}$ .

x \cdot x^{2} - x^{2} - 2 x = 0

$x \cdot x^{2} - x^{2} - 2 x = 0$

Step 1.2

Factor

x

$x$ out of

- x^{2}

$- x^{2}$ .

x \cdot x^{2} + x (- x) - 2 x = 0

$x \cdot x^{2} + x (- x) - 2 x = 0$

Step 1.3

Factor

x

$x$ out of

- 2 x

$- 2 x$ .

x \cdot x^{2} + x (- x) + x \cdot - 2 = 0

$x \cdot x^{2} + x (- x) + x \cdot - 2 = 0$

Step 1.4

Factor

x

$x$ out of

x \cdot x^{2} + x (- x)

$x \cdot x^{2} + x (- x)$ .

x (x^{2} - x) + x \cdot - 2 = 0

$x (x^{2} - x) + x \cdot - 2 = 0$

Step 1.5

Factor

x

$x$ out of

x (x^{2} - x) + x \cdot - 2

$x (x^{2} - x) + x \cdot - 2$ .

x (x^{2} - x - 2) = 0

$x (x^{2} - x - 2) = 0$

x (x^{2} - x - 2) = 0

$x (x^{2} - x - 2) = 0$

Step 2

Factor.

Tap for more steps...

Step 2.1

Factor

x^{2} - x - 2

$x^{2} - x - 2$ using the AC method.

Tap for more steps...

Step 2.1.1

Consider the form

x^{2} + b x + c

$x^{2} + b x + c$ . Find a pair of integers whose product is

c

$c$ and whose sum is

b

$b$ . In this case, whose product is

- 2

$- 2$ and whose sum is

- 1

$- 1$ .

- 2, 1

$- 2, 1$

Step 2.1.2

Write the factored form using these integers.

x ((x - 2) (x + 1)) = 0

$x ((x - 2) (x + 1)) = 0$

x ((x - 2) (x + 1)) = 0

$x ((x - 2) (x + 1)) = 0$

Step 2.2

Remove unnecessary parentheses.

x (x - 2) (x + 1) = 0

$x (x - 2) (x + 1) = 0$

x (x - 2) (x + 1) = 0

$x (x - 2) (x + 1) = 0$

Step 3

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

x = 0

$x = 0$

x - 2 = 0

$x - 2 = 0$

x + 1 = 0

$x + 1 = 0$

Step 4

Set

x

$x$ equal to

0

$0$ .

x = 0

$x = 0$

Step 5

Set

x - 2

$x - 2$ equal to

0

$0$ and solve for

x

$x$ .

Tap for more steps...

Step 5.1

Set

x - 2

$x - 2$ equal to

0

$0$ .

x - 2 = 0

$x - 2 = 0$

Step 5.2

Add

2

$2$ to both sides of the equation.

x = 2

$x = 2$

x = 2

$x = 2$

Step 6

Set

x + 1

$x + 1$ equal to

0

$0$ and solve for

x

$x$ .

Tap for more steps...

Step 6.1

Set

x + 1

$x + 1$ equal to

0

$0$ .

x + 1 = 0

$x + 1 = 0$

Step 6.2

Subtract

1

$1$ from both sides of the equation.

x = - 1

$x = - 1$

x = - 1

$x = - 1$

Step 7

The final solution is all the values that make

x (x - 2) (x + 1) = 0

$x (x - 2) (x + 1) = 0$ true.

x = 0, 2, - 1

$x = 0, 2, - 1$

x^{3} - x^{2} - 2 x = 0

$x^{3} - x^{2} - 2 x = 0$

(

(

)

)

|

|

[

[

]

]

√

√





≥

≥





















7

7

8

8

9

9













≤

≤





















4

4

5

5

6

6

/

/

^

^

×

×

>

>









∩

∩

∪

∪





1

1

2

2

3

3

-

-

+

+

÷

÷

<

<









π

π

∞

∞



,

,

0

0

.

.

%

%



=

=









[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$