Precalculus Examples

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

Step 1

Factor the left side of the equation.

Tap for more steps...

Step 1.1

Factor $x$ out of $x^{3} - 3 x^{2} + 2 x$ .

Tap for more steps...

Step 1.1.1

Factor $x$ out of $x^{3}$ .

$x \cdot x^{2} - 3 x^{2} + 2 x = 0$

Step 1.1.2

Factor $x$ out of $- 3 x^{2}$ .

$x \cdot x^{2} + x (- 3 x) + 2 x = 0$

Step 1.1.3

Factor $x$ out of $2 x$ .

$x \cdot x^{2} + x (- 3 x) + x \cdot 2 = 0$

Step 1.1.4

Factor $x$ out of $x \cdot x^{2} + x (- 3 x)$ .

$x (x^{2} - 3 x) + x \cdot 2 = 0$

Step 1.1.5

Factor $x$ out of $x (x^{2} - 3 x) + x \cdot 2$ .

$x (x^{2} - 3 x + 2) = 0$

Step 1.2

Factor.

Tap for more steps...

Step 1.2.1

Factor $x^{2} - 3 x + 2$ using the AC method.

Tap for more steps...

Step 1.2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $2$ and whose sum is $- 3$ .

$- 2, - 1$

Step 1.2.1.2

Write the factored form using these integers.

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

Step 1.2.2

Remove unnecessary parentheses.

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

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 2 = 0$

$x - 1 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $x - 2$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 4.1

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 4.2

Add $2$ to both sides of the equation.

$x = 2$

Step 5

Set $x - 1$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 5.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 5.2

Add $1$ to both sides of the equation.

$x = 1$

Step 6

The final solution is all the values that make $x (x - 2) (x - 1) = 0$ true.

$x = 0, 2, 1$