Find the x and y Intercepts t(x)=x^2(x-3)(3-x)

$t (x) = x^{2} (x - 3) (3 - x)$

Step 1

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

$x^{2} = 0$

$x - 3 = 0$

$3 - x = 0$

Set $x^{2}$ equal to $0$ and solve for $x$ .

Set $x^{2}$ equal to $0$ .

$x^{2} = 0$

Solve $x^{2} = 0$ for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

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

$x = 0, 3$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Raising $0$ to any positive power yields $0$ .

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

Subtract $3$ from $0$ .

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

Multiply $0$ by $- 3$ .

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

Subtract $0$ from $3$ .

$y = 0 \cdot 3$

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): $(0, 0), (3, 0)$

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

Step 4

Find the x and y Intercepts t(x)=x^2(x-3)(3-x)

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