Find the x and y Intercepts f(x)=(x-5)(x+1)(3x+6)

$f (x) = (x - 5) (x + 1) (3 x + 6)$

Step 1

Find the x-intercepts.

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

$0 = (x - 5) (x + 1) (3 x + 6)$

Solve the equation.

Rewrite the equation as $(x - 5) (x + 1) (3 x + 6) = 0$ .

$(x - 5) (x + 1) (3 x + 6) = 0$

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

$x - 5 = 0$

$x + 1 = 0$

$3 x + 6 = 0$

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

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

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from 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 $x$ .

Subtract $6$ from 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 $(x - 5) (x + 1) (3 x + 6) = 0$ true.

$x = 5, - 1, - 2$

x-intercept(s) in point form.

x-intercept(s): $(5, 0), (- 1, 0), (- 2, 0)$

Step 2

Find the y-intercepts.

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

$y = ((0) - 5) ((0) + 1) (3 (0) + 6)$

Solve the equation.

Remove parentheses.

$y = (0 - 5) ((0) + 1) (3 (0) + 6)$

Remove parentheses.

$y = (0 - 5) (0 + 1) (3 (0) + 6)$

Remove parentheses.

$y = ((0) - 5) ((0) + 1) (3 (0) + 6)$

Simplify $((0) - 5) ((0) + 1) (3 (0) + 6)$ .

Subtract $5$ from $0$ .

$y = - 5 ((0) + 1) (3 (0) + 6)$

Add $0$ and $1$ .

$y = - 5 \cdot 1 (3 (0) + 6)$

Multiply $- 5$ by $1$ .

$y = - 5 (3 (0) + 6)$

Multiply $3$ by $0$ .

$y = - 5 (0 + 6)$

Add $0$ and $6$ .

$y = - 5 \cdot 6$

Multiply $- 5$ by $6$ .

$y = - 30$

y-intercept(s) in point form.

y-intercept(s): $(0, - 30)$

Step 3

List the intersections.

x-intercept(s): $(5, 0), (- 1, 0), (- 2, 0)$

y-intercept(s): $(0, - 30)$

Step 4

Find the x and y Intercepts f(x)=(x-5)(x+1)(3x+6)

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