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

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

Step 1

Write ${(x - 4)}^{2} (x + 4) (x - 1)$ as an equation.

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

Step 2

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

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

$x + 4 = 0$

$x - 1 = 0$

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 $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Set $x + 4$ equal to $0$ and solve for $x$ .

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

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

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

$x = 4, - 4, 1$

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Subtract $4$ from $0$ .

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

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

$y = 16 ((0) + 4) ((0) - 1)$

Add $0$ and $4$ .

$y = 16 \cdot 4 ((0) - 1)$

Multiply $16$ by $4$ .

$y = 64 ((0) - 1)$

Subtract $1$ from $0$ .

$y = 64 \cdot - 1$

Multiply $64$ by $- 1$ .

$y = - 64$

y-intercept(s) in point form.

y-intercept(s): $(0, - 64)$

Step 4

List the intersections.

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

y-intercept(s): $(0, - 64)$

Step 5

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

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