Find the x and y Intercepts f(x)=-2x(x-1)(3x-6)(x-2)

$f (x) = - 2 x (x - 1) (3 x - 6) (x - 2)$

Find the x-intercepts.

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

$0 = - 2 x (x - 1) (3 x - 6) (x - 2)$

Solve the equation.

Rewrite the equation as $- 2 x (x - 1) (3 x - 6) (x - 2) = 0$ .

$- 2 x (x - 1) (3 x - 6) (x - 2) = 0$

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

$x = 0$

$x - 1 = 0$

$3 x - 6 = 0$

$x - 2 = 0$

Set $x$ equal to $0$ .

$x = 0$

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.

$x = 1$

Set $3 x - 6$ equal to $0$ and solve for $x$ .

Set $3 x - 6$ equal to $0$ .

$3 x - 6 = 0$

Solve $3 x - 6 = 0$ for $x$ .

Add $6$ to both sides of the equation.

$3 x = 6$

Divide each term in $3 x = 6$ by $3$ and simplify.

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Divide $x$ by $1$ .

$x = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$

The final solution is all the values that make $- 2 x (x - 1) (3 x - 6) (x - 2) = 0$ true.

$x = 0, 1, 2$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = - 2 \cdot 0 ((0) - 1) (3 (0) - 6) ((0) - 2)$

Solve the equation.

Remove parentheses.

$y = - 2 \cdot (0 (0 - 1) (3 (0) - 6) ((0) - 2))$

Remove parentheses.

$y = - 2 \cdot (0 (0 - 1) (3 (0) - 6) (0 - 2))$

Remove parentheses.

$y = - 2 \cdot (0 ((0) - 1) (3 (0) - 6) ((0) - 2))$

Simplify $- 2 \cdot (0 ((0) - 1) (3 (0) - 6) ((0) - 2))$ .

Subtract $1$ from $0$ .

$y = - 2 \cdot (0 \cdot - 1 (3 (0) - 6) ((0) - 2))$

Multiply $0$ by $- 1$ .

$y = - 2 \cdot (0 (3 (0) - 6) ((0) - 2))$

Multiply $3$ by $0$ .

$y = - 2 \cdot (0 (0 - 6) ((0) - 2))$

Subtract $6$ from $0$ .

$y = - 2 \cdot (0 \cdot - 6 ((0) - 2))$

Multiply $0$ by $- 6$ .

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

Subtract $2$ from $0$ .

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

Multiply $0$ by $- 2$ .

$y = - 2 \cdot 0$

Multiply $- 2$ by $0$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

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

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

Find the x and y Intercepts f(x)=-2x(x-1)(3x-6)(x-2)

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