Algebra Examples

$y = (x + 4) (x + 2) (x - 1) (x - 3)$

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 $x$ .

$0 = (x + 4) (x + 2) (x - 1) (x - 3)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $(x + 4) (x + 2) (x - 1) (x - 3) = 0$ .

$(x + 4) (x + 2) (x - 1) (x - 3) = 0$

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 $0$ .

$x + 4 = 0$

$x + 2 = 0$

$x - 1 = 0$

$x - 3 = 0$

Step 1.2.3

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

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Step 1.2.3.1

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

$x + 4 = 0$

Step 1.2.3.2

Subtract $4$ from both sides of the equation.

$x = - 4$

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

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Step 1.2.5.1

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

$x - 1 = 0$

Step 1.2.5.2

Add $1$ to both sides of the equation.

$x = 1$

Step 1.2.6

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

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Step 1.2.6.1

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

$x - 3 = 0$

Step 1.2.6.2

Add $3$ to both sides of the equation.

$x = 3$

Step 1.2.7

The final solution is all the values that make $(x + 4) (x + 2) (x - 1) (x - 3) = 0$ true.

$x = - 4, - 2, 1, 3$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 4, 0), (- 2, 0), (1, 0), (3, 0)$

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 $y$ .

$y = ((0) + 4) ((0) + 2) ((0) - 1) ((0) - 3)$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = (0 + 4) ((0) + 2) ((0) - 1) ((0) - 3)$

Step 2.2.2

Remove parentheses.

$y = (0 + 4) (0 + 2) ((0) - 1) ((0) - 3)$

Step 2.2.3

Remove parentheses.

$y = (0 + 4) (0 + 2) (0 - 1) ((0) - 3)$

Step 2.2.4

Remove parentheses.

$y = (0 + 4) (0 + 2) (0 - 1) (0 - 3)$

Step 2.2.5

Remove parentheses.

$y = ((0) + 4) ((0) + 2) ((0) - 1) ((0) - 3)$

Step 2.2.6

Simplify $((0) + 4) ((0) + 2) ((0) - 1) ((0) - 3)$ .

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Step 2.2.6.1

Add $0$ and $4$ .

$y = 4 ((0) + 2) ((0) - 1) ((0) - 3)$

Step 2.2.6.2

Add $0$ and $2$ .

$y = 4 \cdot 2 ((0) - 1) ((0) - 3)$

Step 2.2.6.3

Multiply $4$ by $2$ .

$y = 8 ((0) - 1) ((0) - 3)$

Step 2.2.6.4

Subtract $1$ from $0$ .

$y = 8 \cdot - 1 ((0) - 3)$

Step 2.2.6.5

Multiply $8$ by $- 1$ .

$y = - 8 ((0) - 3)$

Step 2.2.6.6

Subtract $3$ from $0$ .

$y = - 8 \cdot - 3$

Step 2.2.6.7

Multiply $- 8$ by $- 3$ .

$y = 24$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 24)$

Step 3

List the intersections.

x-intercept(s): $(- 4, 0), (- 2, 0), (1, 0), (3, 0)$

y-intercept(s): $(0, 24)$

Step 4