Find the x and y Intercepts x^5-3x^4

$x^{5} - 3 x^{4}$

Step 1

Write $x^{5} - 3 x^{4}$ as an equation.

$y = x^{5} - 3 x^{4}$

Step 2

Find the x-intercepts.

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

$0 = x^{5} - 3 x^{4}$

Solve the equation.

Rewrite the equation as $x^{5} - 3 x^{4} = 0$ .

$x^{5} - 3 x^{4} = 0$

Factor $x^{4}$ out of $x^{5} - 3 x^{4}$ .

Factor $x^{4}$ out of $x^{5}$ .

$x^{4} x - 3 x^{4} = 0$

Factor $x^{4}$ out of $- 3 x^{4}$ .

$x^{4} x + x^{4} \cdot - 3 = 0$

Factor $x^{4}$ out of $x^{4} x + x^{4} \cdot - 3$ .

$x^{4} (x - 3) = 0$

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

$x^{4} = 0$

$x - 3 = 0$

Set $x^{4}$ equal to $0$ and solve for $x$ .

Set $x^{4}$ equal to $0$ .

$x^{4} = 0$

Solve $x^{4} = 0$ for $x$ .

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

$x = \pm \sqrt[4]{0}$

Simplify $\pm \sqrt[4]{0}$ .

Rewrite $0$ as $0^{4}$ .

$x = \pm \sqrt[4]{0^{4}}$

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 $x^{4} (x - 3) = 0$ true.

$x = 0, 3$

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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

$y = {(0)}^{5} - 3 {(0)}^{4}$

Solve the equation.

Remove parentheses.

$y = 0^{5} - 3 {(0)}^{4}$

Remove parentheses.

$y = 0^{5} - 3 \cdot 0^{4}$

Remove parentheses.

$y = {(0)}^{5} - 3 {(0)}^{4}$

Simplify ${(0)}^{5} - 3 {(0)}^{4}$ .

Simplify each term.

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

$y = 0 - 3 {(0)}^{4}$

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

$y = 0 - 3 \cdot 0$

Multiply $- 3$ by $0$ .

$y = 0 + 0$

Add $0$ and $0$ .

$y = 0$

y-intercept(s) in point form.

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

Step 4

List the intersections.

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

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

Step 5

Find the x and y Intercepts x^5-3x^4

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