Find the x and y Intercepts f(x)=(3x+6)(x^2+3)

$f (x) = (3 x + 6) (x^{2} + 3)$

Find the x-intercepts.

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

$0 = (3 x + 6) (x^{2} + 3)$

Solve the equation.

Rewrite the equation as $(3 x + 6) (x^{2} + 3) = 0$ .

$(3 x + 6) (x^{2} + 3) = 0$

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

$3 x + 6 = 0$

$x^{2} + 3 = 0$

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 $3$ .

$x = - 2$

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

Set $x^{2} + 3$ equal to $0$ .

$x^{2} + 3 = 0$

Solve $x^{2} + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$x^{2} = - 3$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{- 3}$

Simplify $\pm \sqrt{- 3}$ .

Rewrite $- 3$ as $- 1 (3)$ .

$x = \pm \sqrt{- 1 (3)}$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{3}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = i \sqrt{3}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - i \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = i \sqrt{3}, - i \sqrt{3}$

The final solution is all the values that make $(3 x + 6) (x^{2} + 3) = 0$ true.

$x = - 2, i \sqrt{3}, - i \sqrt{3}$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = (3 (0) + 6) ({(0)}^{2} + 3)$

Solve the equation.

Remove parentheses.

$y = (3 (0) + 6) (0^{2} + 3)$

Remove parentheses.

$y = (3 (0) + 6) ({(0)}^{2} + 3)$

Simplify $(3 (0) + 6) ({(0)}^{2} + 3)$ .

Multiply $3$ by $0$ .

$y = (0 + 6) ({(0)}^{2} + 3)$

Add $0$ and $6$ .

$y = 6 ({(0)}^{2} + 3)$

Raising $0$ to any positive power yields $0$ .

$y = 6 (0 + 3)$

Add $0$ and $3$ .

$y = 6 \cdot 3$

Multiply $6$ by $3$ .

$y = 18$

y-intercept(s) in point form.

y-intercept(s): $(0, 18)$

List the intersections.

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

y-intercept(s): $(0, 18)$

Find the x and y Intercepts f(x)=(3x+6)(x^2+3)

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