Find the x and y Intercepts f(x)=x(x+5)^2(x+3)

$f (x) = x {(x + 5)}^{2} (x + 3)$

Step 1

Find the x-intercepts.

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

$0 = x {(x + 5)}^{2} (x + 3)$

Solve the equation.

Rewrite the equation as $x {(x + 5)}^{2} (x + 3) = 0$ .

$x {(x + 5)}^{2} (x + 3) = 0$

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

$x = 0$

${(x + 5)}^{2} = 0$

$x + 3 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set ${(x + 5)}^{2}$ equal to $0$ and solve for $x$ .

Set ${(x + 5)}^{2}$ equal to $0$ .

${(x + 5)}^{2} = 0$

Solve ${(x + 5)}^{2} = 0$ for $x$ .

Set the $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

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.

$x = - 3$

The final solution is all the values that make $x {(x + 5)}^{2} (x + 3) = 0$ true.

$x = 0, - 5, - 3$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- 5, 0), (- 3, 0)$

Step 2

Find the y-intercepts.

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

$y = (0) {((0) + 5)}^{2} ((0) + 3)$

Solve the equation.

Remove parentheses.

$y = 0 {(0 + 5)}^{2} ((0) + 3)$

Remove parentheses.

$y = 0 {(0 + 5)}^{2} (0 + 3)$

Remove parentheses.

$y = (0) {((0) + 5)}^{2} ((0) + 3)$

Simplify $(0) {((0) + 5)}^{2} ((0) + 3)$ .

Add $0$ and $5$ .

$y = 0 \cdot 5^{2} ((0) + 3)$

Raise $5$ to the power of $2$ .

$y = 0 \cdot 25 ((0) + 3)$

Multiply $0$ by $25$ .

$y = 0 ((0) + 3)$

Add $0$ and $3$ .

$y = 0 \cdot 3$

Multiply $0$ by $3$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(0, 0), (- 5, 0), (- 3, 0)$

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

Step 4

Find the x and y Intercepts f(x)=x(x+5)^2(x+3)

Related Questions

Support LCMGCF.com by disabling your adblocker.