Exercise 16 Page 348

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=3x(x+2)^3

WriteDiff

Write as a difference

y=3(x-0)(x+2)^3

a+b=a-(- b)

y=3(x-0)(x-(- 2))^3

Let's now use a table to organize the information. Note that, since 3≠ 0, then 3 cannot be a zero of the polynomial.

Factor	Appearances	Zero	Multiplicity
x- 0	1	0	1
x-( - 2 )	3	- 2	3

We can say that 0 is a zero of multiplicity 1, and - 2 is a zero of multiplicity 3.