Find the x and y Intercepts (x+1)(x-3)(x-4)

$(x + 1) (x - 3) (x - 4)$

Step 1

Write $(x + 1) (x - 3) (x - 4)$ as an equation.

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

Step 2

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

$x + 1 = 0$

$x - 3 = 0$

$x - 4 = 0$

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

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

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

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

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

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

$x = - 1, 3, 4$

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Add $0$ and $1$ .

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

Multiply $(0) - 3$ by $1$ .

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

Subtract $3$ from $0$ .

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

Subtract $4$ from $0$ .

$y = - 3 \cdot - 4$

Multiply $- 3$ by $- 4$ .

$y = 12$

y-intercept(s) in point form.

y-intercept(s): $(0, 12)$

Step 4

List the intersections.

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

y-intercept(s): $(0, 12)$

Step 5

Find the x and y Intercepts (x+1)(x-3)(x-4)

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