Identify the Zeros and Their Multiplicities f(x)=6(x^2-5)^3

$f (x) = 6 {(x^{2} - 5)}^{3}$

Step 1

Set $6 {(x^{2} - 5)}^{3}$ equal to $0$ .

$6 {(x^{2} - 5)}^{3} = 0$

Step 2

Solve for $x$ .

Divide each term in $6 {(x^{2} - 5)}^{3} = 0$ by $6$ and simplify.

Divide each term in $6 {(x^{2} - 5)}^{3} = 0$ by $6$ .

$\frac{6 {(x^{2} - 5)}^{3}}{6} = \frac{0}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 {(x^{2} - 5)}^{3}}{6} = \frac{0}{6}$

Divide ${(x^{2} - 5)}^{3}$ by $1$ .

${(x^{2} - 5)}^{3} = \frac{0}{6}$

Simplify the right side.

Divide $0$ by $6$ .

${(x^{2} - 5)}^{3} = 0$

Set the $x^{2} - 5$ equal to $0$ .

$x^{2} - 5 = 0$

Solve for $x$ .

Add $5$ to both sides of the equation.

$x^{2} = 5$

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

$x = \pm \sqrt{5}$

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.

$x = \sqrt{5}$

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

$x = - \sqrt{5}$

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

$x = \sqrt{5}, - \sqrt{5}$ (Multiplicity of $3$ )

Step 3