Write a polynomial function in standard form with real coefficients whose zeros and their multiplicities include those listed. Graph it and write down your observations of it. -3(multiplicity 2 ), 2(multiplicity 3)

Question

anonymous · Answer

do you know what "multiplicity" means in this context?

anonymous · Answer

no

anonymous · Answer

How do I become Moderator?

anonymous · Answer

it means the factor as that number as an exponent
so the factor that has a zero of $-3$ is $x+3$ and since the multiplicity is 2, it is 
$$(x+3)^2$$

anonymous · Answer

multiplicity is a factor that repeats more than once

anonymous · Answer

right
so one factor will be $(x+3)^2$ and the other will be $(x-2)^3$ giving you 
$$f(x)=(x+3)^2(x-2)^3$$

anonymous · Answer

so for -3(multiplicity 2) will it be (X-3) to the second power

anonymous · Answer

no, not quite

anonymous · Answer

it will be $(x+3)^2$

anonymous · Answer

if $x=-3$ then $x+3=0$ so the factor is $(x+3)^2$ not $(x-3)^2$

anonymous · Answer

oook