Find the x and y Intercepts P(x)=(x-1)^2(x-5)

$P (x) = {(x - 1)}^{2} (x - 5)$

Find the x-intercepts.

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

$0 = {(x - 1)}^{2} (x - 5)$

Solve the equation.

Rewrite the equation as ${(x - 1)}^{2} (x - 5) = 0$ .

${(x - 1)}^{2} (x - 5) = 0$

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

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

$x - 5 = 0$

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 $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

The final solution is all the values that make ${(x - 1)}^{2} (x - 5) = 0$ true.

$x = 1, 5$

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (5, 0)$

Find the y-intercepts.

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

$y = {((0) - 1)}^{2} ((0) - 5)$

Solve the equation.

Remove parentheses.

$y = {(0 - 1)}^{2} ((0) - 5)$

Remove parentheses.

$y = {(0 - 1)}^{2} (0 - 5)$

Remove parentheses.

$y = {((0) - 1)}^{2} ((0) - 5)$

Simplify ${((0) - 1)}^{2} ((0) - 5)$ .

Subtract $1$ from $0$ .

$y = {(- 1)}^{2} ((0) - 5)$

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

$y = 1 ((0) - 5)$

Multiply $(0) - 5$ by $1$ .

$y = (0) - 5$

Subtract $5$ from $0$ .

$y = - 5$

y-intercept(s) in point form.

y-intercept(s): $(0, - 5)$

List the intersections.

x-intercept(s): $(1, 0), (5, 0)$

y-intercept(s): $(0, - 5)$

Find the x and y Intercepts P(x)=(x-1)^2(x-5)

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