Find the x and y Intercepts P(x)=(x+1)(x-2)(x-4)

$P (x) = (x + 1) (x - 2) (x - 4)$

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

$x + 1 = 0$

$x - 2 = 0$

$x - 4 = 0$

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

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 $(x + 1) (x - 2) (x - 4) = 0$ true.

$x = - 1, 2, 4$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Add $0$ and $1$ .

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

Multiply $(0) - 2$ by $1$ .

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

Subtract $2$ from $0$ .

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

Subtract $4$ from $0$ .

$y = - 2 \cdot - 4$

Multiply $- 2$ by $- 4$ .

$y = 8$

y-intercept(s) in point form.

y-intercept(s): $(0, 8)$

List the intersections.

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

y-intercept(s): $(0, 8)$

Find the x and y Intercepts P(x)=(x+1)(x-2)(x-4)

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