Find the x and y Intercepts f(x)=(x+4)^2(x-2)^5(x-1)

$f (x) = {(x + 4)}^{2} {(x - 2)}^{5} (x - 1)$

Find the x-intercepts.

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

$0 = {(x + 4)}^{2} {(x - 2)}^{5} (x - 1)$

Solve the equation.

Rewrite the equation as ${(x + 4)}^{2} {(x - 2)}^{5} (x - 1) = 0$ .

${(x + 4)}^{2} {(x - 2)}^{5} (x - 1) = 0$

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

${(x + 4)}^{2} = 0$

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

$x - 1 = 0$

Set ${(x + 4)}^{2}$ equal to $0$ and solve for $x$ .

Set ${(x + 4)}^{2}$ equal to $0$ .

${(x + 4)}^{2} = 0$

Solve ${(x + 4)}^{2} = 0$ for $x$ .

Set the $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

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

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

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

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

Set the $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

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 ${(x + 4)}^{2} {(x - 2)}^{5} (x - 1) = 0$ true.

$x = - 4, 2, 1$

x-intercept(s) in point form.

x-intercept(s): $(- 4, 0), (2, 0), (1, 0)$

Find the y-intercepts.

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

$y = {((0) + 4)}^{2} {((0) - 2)}^{5} ((0) - 1)$

Solve the equation.

Remove parentheses.

$y = {(0 + 4)}^{2} {((0) - 2)}^{5} ((0) - 1)$

Remove parentheses.

$y = {(0 + 4)}^{2} {(0 - 2)}^{5} ((0) - 1)$

Remove parentheses.

$y = {(0 + 4)}^{2} {(0 - 2)}^{5} (0 - 1)$

Remove parentheses.

$y = {((0) + 4)}^{2} {((0) - 2)}^{5} ((0) - 1)$

Simplify ${((0) + 4)}^{2} {((0) - 2)}^{5} ((0) - 1)$ .

Add $0$ and $4$ .

$y = 4^{2} {((0) - 2)}^{5} ((0) - 1)$

Raise $4$ to the power of $2$ .

$y = 16 {((0) - 2)}^{5} ((0) - 1)$

Subtract $2$ from $0$ .

$y = 16 {(- 2)}^{5} ((0) - 1)$

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

$y = 16 \cdot - 32 ((0) - 1)$

Multiply $16$ by $- 32$ .

$y = - 512 ((0) - 1)$

Subtract $1$ from $0$ .

$y = - 512 \cdot - 1$

Multiply $- 512$ by $- 1$ .

$y = 512$

y-intercept(s) in point form.

y-intercept(s): $(0, 512)$

List the intersections.

x-intercept(s): $(- 4, 0), (2, 0), (1, 0)$

y-intercept(s): $(0, 512)$

Find the x and y Intercepts f(x)=(x+4)^2(x-2)^5(x-1)

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