Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Factor $x$ out of $2 x$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Factor.

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Step 2.1

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

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Step 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 $3$ .

$1, 2$

Step 2.1.2

Write the factored form using these integers.

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

Step 2.2

Remove unnecessary parentheses.

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

Step 3

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

$x = 0$

$x + 1 = 0$

$x + 2 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

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

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Step 5.1

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

$x + 1 = 0$

Step 5.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 6

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

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Step 6.1

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

$x + 2 = 0$

Step 6.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 7

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

$x = 0, - 1, - 2$