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

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

Step 1

Write $(x + 2) {(x - 1)}^{2} {(x + 1)}^{2}$ as an equation.

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

Step 2

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

$x + 2 = 0$

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

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

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

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

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

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

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

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

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

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

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

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

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

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

$x = - 2, 1, - 1$

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Add $0$ and $2$ .

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

Subtract $1$ from $0$ .

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

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

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

Multiply $2$ by $1$ .

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

Add $0$ and $1$ .

$y = 2 \cdot 1^{2}$

One to any power is one.

$y = 2 \cdot 1$

Multiply $2$ by $1$ .

$y = 2$

y-intercept(s) in point form.

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

Step 4

List the intersections.

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

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

Step 5

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

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