We say that b is a zero of multiplicity n when (x-b) appears n times as a factor of a polynomial.
Zeros of Multiplicity 1: 5 Zero of Multiplicity 2: - 2
Practice makes perfect
We want to determine the zeros of the given polynomial function as well as their multiplicity. We say that b is a zero of multiplicity n when (x- b) appears n times as a factor of a polynomial. Let's rewrite the given function in order to find the zeros.
y=(x-5)(x+2)^2
a+b=a-(- b)
y=(x-5)( x-(- 2))^2
Let's now use a table to organize the information.
Factor
Appearances
Zero
Multiplicity
x- 5
1
5
1
x-( - 2 )
2
- 2
2
We can say that 5 is a zero of multiplicity 1, and - 2 is a zero of multiplicity 2.
