Find the x and y Intercepts (x-3)^2(x+2)(x-4)

${(x - 3)}^{2} (x + 2) (x - 4)$

Step 1

Write ${(x - 3)}^{2} (x + 2) (x - 4)$ as an equation.

$y = {(x - 3)}^{2} (x + 2) (x - 4)$

Step 2

Find the x-intercepts.

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

$0 = {(x - 3)}^{2} (x + 2) (x - 4)$

Solve the equation.

Rewrite the equation as ${(x - 3)}^{2} (x + 2) (x - 4) = 0$ .

${(x - 3)}^{2} (x + 2) (x - 4) = 0$

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

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

$x + 2 = 0$

$x - 4 = 0$

Set ${(x - 3)}^{2}$ equal to $0$ and solve for $x$ .

Set ${(x - 3)}^{2}$ equal to $0$ .

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

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

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

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

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make ${(x - 3)}^{2} (x + 2) (x - 4) = 0$ true.

$x = 3, - 2, 4$

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (- 2, 0), (4, 0)$

Step 3

Find the y-intercepts.

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

$y = {((0) - 3)}^{2} ((0) + 2) ((0) - 4)$

Solve the equation.

Remove parentheses.

$y = {(0 - 3)}^{2} ((0) + 2) ((0) - 4)$

Remove parentheses.

$y = {(0 - 3)}^{2} (0 + 2) ((0) - 4)$

Remove parentheses.

$y = {(0 - 3)}^{2} (0 + 2) (0 - 4)$

Remove parentheses.

$y = {((0) - 3)}^{2} ((0) + 2) ((0) - 4)$

Simplify ${((0) - 3)}^{2} ((0) + 2) ((0) - 4)$ .

Subtract $3$ from $0$ .

$y = {(- 3)}^{2} ((0) + 2) ((0) - 4)$

Raise $- 3$ to the power of $2$ .

$y = 9 ((0) + 2) ((0) - 4)$

Add $0$ and $2$ .

$y = 9 \cdot 2 ((0) - 4)$

Multiply $9$ by $2$ .

$y = 18 ((0) - 4)$

Subtract $4$ from $0$ .

$y = 18 \cdot - 4$

Multiply $18$ by $- 4$ .

$y = - 72$

y-intercept(s) in point form.

y-intercept(s): $(0, - 72)$

Step 4

List the intersections.

x-intercept(s): $(3, 0), (- 2, 0), (4, 0)$

y-intercept(s): $(0, - 72)$

Step 5

Find the x and y Intercepts (x-3)^2(x+2)(x-4)

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