Question

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

Answer 1

`x=2" multiplicity 4", x=3" multiplicity 1"`

Explanation:

`"zeros are the values of x that make " f(x)=0`

`"solve " (x-2)^4(x-3)=0`

`"equate each factor to zero"`

`(x-2)=0rArrx=2`

`rArr(x-2)^4=0rArrx=2larr" 4 times"`

`x-3=0rArrx=3larr" 1 only"`

`rArrx=2" with multiplicity 4"`

`"and " x=3" with multiplicity 1"`