Question

Please help me with this problem, I will give a medal =)
What are the zeroes of the function? What are their multiplicities?

f(x)=3x^3+15x^2+18x

A. The numbers 3, –2, and 0 are zeroes of multiplicity 2.
B. The numbers 3, –2, and 0 are zeroes of multiplicity 1.
C. The numbers –3, –2, and 0 are zeroes of multiplicity 1.
D. The numbers –3, –2, and 0 are zeroes of multiplicity 2.
I know it is C or D but I can't figure out the multiplicities part. :(

Answer 1

Start by factoring it.
What did you get as the factors?

Answer 2

graph is here
i got the zeroes -3, -2, and 0

Answer 3

but what are multiplicities?

Answer 4

This should help you :-)
http://users.stlcc.edu/amosher/PolyZerosThms.htm

Answer 5

If a factored equation has the same factor more than once, that factor has a multiplicity.
For example, the equation:
x³ + x² - 5x + 3
factors to:
(x-1)(x-1)(x+3)

Since the root x=1 shows up twice, we say that the root x=1 has multiplicity 2.

Answer 6

Is it C?

Answer 7

Yes

Answer 8

Thanks :D