Algebra Examples

$f (x) = x (x + 2) (x - 3) (x + 4)$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = x (x + 2) (x - 3) (x + 4)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $x (x + 2) (x - 3) (x + 4) = 0$ .

$x (x + 2) (x - 3) (x + 4) = 0$

Step 1.2.2

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

$x = 0$

$x + 2 = 0$

$x - 3 = 0$

$x + 4 = 0$

Step 1.2.3

Set $x$ equal to $0$ .

$x = 0$

Step 1.2.4

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

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Step 1.2.4.1

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

$x + 2 = 0$

Step 1.2.4.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 1.2.5

Set $x - 3$ equal to $0$ and solve for $x$ .

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Step 1.2.5.1

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Step 1.2.5.2

Add $3$ to both sides of the equation.

$x = 3$

Step 1.2.6

Set $x + 4$ equal to $0$ and solve for $x$ .

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Step 1.2.6.1

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Step 1.2.6.2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 1.2.7

The final solution is all the values that make $x (x + 2) (x - 3) (x + 4) = 0$ true.

$x = 0, - 2, 3, - 4$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- 2, 0), (3, 0), (- 4, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = (0) ((0) + 2) ((0) - 3) ((0) + 4)$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 0 (0 + 2) ((0) - 3) ((0) + 4)$

Step 2.2.2

Remove parentheses.

$y = 0 (0 + 2) (0 - 3) ((0) + 4)$

Step 2.2.3

Remove parentheses.

$y = 0 (0 + 2) (0 - 3) (0 + 4)$

Step 2.2.4

Remove parentheses.

$y = (0) ((0) + 2) ((0) - 3) ((0) + 4)$

Step 2.2.5

Simplify $(0) ((0) + 2) ((0) - 3) ((0) + 4)$ .

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Step 2.2.5.1

Add $0$ and $2$ .

$y = 0 \cdot 2 ((0) - 3) ((0) + 4)$

Step 2.2.5.2

Multiply $0$ by $2$ .

$y = 0 ((0) - 3) ((0) + 4)$

Step 2.2.5.3

Subtract $3$ from $0$ .

$y = 0 \cdot - 3 ((0) + 4)$

Step 2.2.5.4

Multiply $0$ by $- 3$ .

$y = 0 ((0) + 4)$

Step 2.2.5.5

Add $0$ and $4$ .

$y = 0 \cdot 4$

Step 2.2.5.6

Multiply $0$ by $4$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

Step 3

List the intersections.

x-intercept(s): $(0, 0), (- 2, 0), (3, 0), (- 4, 0)$

y-intercept(s): $(0, 0)$

Step 4