# How do you find the zeros and multiplicity of f(x)=(x-2)^4(x-3)?

May 25, 2017

$x = 2 \text{ multiplicity 4", x=3" multiplicity 1}$

#### Explanation:

$\text{zeros are the values of x that make } f \left(x\right) = 0$

$\text{solve } {\left(x - 2\right)}^{4} \left(x - 3\right) = 0$

$\text{equate each factor to zero}$

$\left(x - 2\right) = 0 \Rightarrow x = 2$

$\Rightarrow {\left(x - 2\right)}^{4} = 0 \Rightarrow x = 2 \leftarrow \text{ 4 times}$

$x - 3 = 0 \Rightarrow x = 3 \leftarrow \text{ 1 only}$

$\Rightarrow x = 2 \text{ with multiplicity 4}$

$\text{and " x=3" with multiplicity 1}$