Find the x and y Intercepts y=-(x+5)(2x+3)(x-2)(x-4)

$y = - (x + 5) (2 x + 3) (x - 2) (x - 4)$

Step 1

Find the x-intercepts.

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

$0 = - (x + 5) (2 x + 3) (x - 2) (x - 4)$

Solve the equation.

Rewrite the equation as $- (x + 5) (2 x + 3) (x - 2) (x - 4) = 0$ .

$- (x + 5) (2 x + 3) (x - 2) (x - 4) = 0$

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

$x + 5 = 0$

$2 x + 3 = 0$

$x - 2 = 0$

$x - 4 = 0$

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

Set $2 x + 3$ equal to $0$ and solve for $x$ .

Set $2 x + 3$ equal to $0$ .

$2 x + 3 = 0$

Solve $2 x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$2 x = - 3$

Divide each term in $2 x = - 3$ by $2$ and simplify.

Divide each term in $2 x = - 3$ by $2$ .

$\frac{2 x}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 3}{2}$

Divide $x$ by $1$ .

$x = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

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

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

$x - 2 = 0$

Add $2$ to 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 $- (x + 5) (2 x + 3) (x - 2) (x - 4) = 0$ true.

$x = - 5, - \frac{3}{2}, 2, 4$

x-intercept(s) in point form.

x-intercept(s): $(- 5, 0), (- \frac{3}{2}, 0), (2, 0), (4, 0)$

Step 2

Find the y-intercepts.

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

$y = - ((0) + 5) (2 (0) + 3) ((0) - 2) ((0) - 4)$

Solve the equation.

Remove parentheses.

$y = - (0 + 5) (2 (0) + 3) ((0) - 2) ((0) - 4)$

Remove parentheses.

$y = - (0 + 5) (2 (0) + 3) (0 - 2) ((0) - 4)$

Remove parentheses.

$y = - (0 + 5) (2 (0) + 3) (0 - 2) (0 - 4)$

Remove parentheses.

$y = - ((0) + 5) (2 (0) + 3) ((0) - 2) ((0) - 4)$

Simplify $- ((0) + 5) (2 (0) + 3) ((0) - 2) ((0) - 4)$ .

Add $0$ and $5$ .

$y = - 1 \cdot 5 (2 (0) + 3) ((0) - 2) ((0) - 4)$

Multiply $- 1$ by $5$ .

$y = - 5 (2 (0) + 3) ((0) - 2) ((0) - 4)$

Multiply $2$ by $0$ .

$y = - 5 (0 + 3) ((0) - 2) ((0) - 4)$

Add $0$ and $3$ .

$y = - 5 \cdot 3 ((0) - 2) ((0) - 4)$

Multiply $- 5$ by $3$ .

$y = - 15 ((0) - 2) ((0) - 4)$

Subtract $2$ from $0$ .

$y = - 15 \cdot - 2 ((0) - 4)$

Multiply $- 15$ by $- 2$ .

$y = 30 ((0) - 4)$

Subtract $4$ from $0$ .

$y = 30 \cdot - 4$

Multiply $30$ by $- 4$ .

$y = - 120$

y-intercept(s) in point form.

y-intercept(s): $(0, - 120)$

Step 3

List the intersections.

x-intercept(s): $(- 5, 0), (- \frac{3}{2}, 0), (2, 0), (4, 0)$

y-intercept(s): $(0, - 120)$

Step 4

Find the x and y Intercepts y=-(x+5)(2x+3)(x-2)(x-4)

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