Find the x and y Intercepts P(x)=(x-2)^2(x-7)

$P (x) = {(x - 2)}^{2} (x - 7)$

Step 1

Find the x-intercepts.

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

$0 = {(x - 2)}^{2} (x - 7)$

Solve the equation.

Rewrite the equation as ${(x - 2)}^{2} (x - 7) = 0$ .

${(x - 2)}^{2} (x - 7) = 0$

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

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

$x - 7 = 0$

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

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

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

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Set $x - 7$ equal to $0$ and solve for $x$ .

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

The final solution is all the values that make ${(x - 2)}^{2} (x - 7) = 0$ true.

$x = 2, 7$

x-intercept(s) in point form.

x-intercept(s): $(2, 0), (7, 0)$

Step 2

Find the y-intercepts.

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

$y = {((0) - 2)}^{2} ((0) - 7)$

Solve the equation.

Remove parentheses.

$y = {(0 - 2)}^{2} ((0) - 7)$

Remove parentheses.

$y = {(0 - 2)}^{2} (0 - 7)$

Remove parentheses.

$y = {((0) - 2)}^{2} ((0) - 7)$

Simplify ${((0) - 2)}^{2} ((0) - 7)$ .

Subtract $2$ from $0$ .

$y = {(- 2)}^{2} ((0) - 7)$

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

$y = 4 ((0) - 7)$

Subtract $7$ from $0$ .

$y = 4 \cdot - 7$

Multiply $4$ by $- 7$ .

$y = - 28$

y-intercept(s) in point form.

y-intercept(s): $(0, - 28)$

Step 3

List the intersections.

x-intercept(s): $(2, 0), (7, 0)$

y-intercept(s): $(0, - 28)$

Step 4

Find the x and y Intercepts P(x)=(x-2)^2(x-7)

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