Find the x and y Intercepts f(x)=(x+3)(x+1)^2(x-1)

$f (x) = (x + 3) {(x + 1)}^{2} (x - 1)$

Step 1

Find the x-intercepts.

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

$0 = (x + 3) {(x + 1)}^{2} (x - 1)$

Solve the equation.

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

$(x + 3) {(x + 1)}^{2} (x - 1) = 0$

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

$x + 3 = 0$

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

$x - 1 = 0$

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

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

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.

$x = - 1$

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

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

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

$x = - 3, - 1, 1$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = ((0) + 3) {((0) + 1)}^{2} ((0) - 1)$

Solve the equation.

Remove parentheses.

$y = (0 + 3) {((0) + 1)}^{2} ((0) - 1)$

Remove parentheses.

$y = (0 + 3) {(0 + 1)}^{2} ((0) - 1)$

Remove parentheses.

$y = (0 + 3) {(0 + 1)}^{2} (0 - 1)$

Remove parentheses.

$y = ((0) + 3) {((0) + 1)}^{2} ((0) - 1)$

Simplify $((0) + 3) {((0) + 1)}^{2} ((0) - 1)$ .

Add $0$ and $3$ .

$y = 3 {((0) + 1)}^{2} ((0) - 1)$

Add $0$ and $1$ .

$y = 3 \cdot 1^{2} ((0) - 1)$

One to any power is one.

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

Multiply $3$ by $1$ .

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

Subtract $1$ from $0$ .

$y = 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$y = - 3$

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

Step 3

List the intersections.

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

y-intercept(s): $(0, - 3)$

Step 4

Find the x and y Intercepts f(x)=(x+3)(x+1)^2(x-1)

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