Find Where Undefined/Discontinuous (30k^3+80k^2)/(10k^2)

$\frac{30 k^{3} + 80 k^{2}}{10 k^{2}}$

Step 1

Set the denominator in $\frac{30 k^{3} + 80 k^{2}}{10 k^{2}}$ equal to $0$ to find where the expression is undefined.

$10 k^{2} = 0$

Step 2

Solve for $k$ .

Divide each term in $10 k^{2} = 0$ by $10$ and simplify.

Divide each term in $10 k^{2} = 0$ by $10$ .

$\frac{10 k^{2}}{10} = \frac{0}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 k^{2}}{10} = \frac{0}{10}$

Divide $k^{2}$ by $1$ .

$k^{2} = \frac{0}{10}$

Simplify the right side.

Divide $0$ by $10$ .

$k^{2} = 0$

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

$k = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$k = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$k = \pm 0$

Plus or minus $0$ is $0$ .

$k = 0$

Step 3