Find the x and y Intercepts f(x)=(x+1)(x-1)^2(x-2)

$f (x) = (x + 1) {(x - 1)}^{2} (x - 2)$

Find the x-intercepts.

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

$0 = (x + 1) {(x - 1)}^{2} (x - 2)$

Solve the equation.

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Rewrite the equation as $(x + 1) {(x - 1)}^{2} (x - 2) = 0$ .

$(x + 1) {(x - 1)}^{2} (x - 2) = 0$

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

$x + 1 = 0$

${(x - 1)}^{2} = 0$

$x - 2 = 0$

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

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Set ${(x - 1)}^{2}$ equal to $0$ and solve for $x$ .

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Set ${(x - 1)}^{2}$ equal to $0$ .

${(x - 1)}^{2} = 0$

Solve ${(x - 1)}^{2} = 0$ for $x$ .

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

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

$x = - 1, 1, 2$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = ((0) + 1) {((0) - 1)}^{2} ((0) - 2)$

Solve the equation.

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Remove parentheses.

$y = (0 + 1) {((0) - 1)}^{2} ((0) - 2)$

Remove parentheses.

$y = (0 + 1) {(0 - 1)}^{2} ((0) - 2)$

Remove parentheses.

$y = (0 + 1) {(0 - 1)}^{2} (0 - 2)$

Remove parentheses.

$y = ((0) + 1) {((0) - 1)}^{2} ((0) - 2)$

Simplify $((0) + 1) {((0) - 1)}^{2} ((0) - 2)$ .

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Add $0$ and $1$ .

$y = 1 {((0) - 1)}^{2} ((0) - 2)$

Multiply ${((0) - 1)}^{2}$ by $1$ .

$y = {((0) - 1)}^{2} ((0) - 2)$

Subtract $1$ from $0$ .

$y = {(- 1)}^{2} ((0) - 2)$

Raise $- 1$ to the power of $2$ .

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

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

$y = (0) - 2$

Subtract $2$ from $0$ .

$y = - 2$

y-intercept(s) in point form.

y-intercept(s): $(0, - 2)$

List the intersections.

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

y-intercept(s): $(0, - 2)$