Find the zeros of f(x) and state the multiplicity of each zero.

$$f(x)=x^5+2x^4+x^3$$

Question

Find the zeros of f(x) and state the multiplicity of each zero.

$$f(x)=x^5+2x^4+x^3$$

anonymous · Answer

factor out the $x^3$ first, telling one zero is 0, and it has multiplicity 3

anonymous · Answer

$$f(x)=x^3(x+1)^2$$
Why do we say 0 is a zero of multiplicity 3 is that not contradictory?

anonymous · Answer

you get 
$$f(x)=x^3(x^2+2x+1)$$ then factor again and get 
$$f(x)=x^3(x+1)^2$$ so your two zeroes are 0 with multiplicity 3 and -1 with multiplicity 2

anonymous · Answer

"multiplicity" means the exponent on the factored term

anonymous · Answer

but why would 0 be a zero?

anonymous · Answer

so  for example $(x-2)^2(x+3)^4$ as two zeros, 2 and -3
2 has multiplicity 2 and -3 has multiplicity 4

anonymous · Answer

because $f(0)=0$ right?

anonymous · Answer

yes

anonymous · Answer

each term has an $x$ in it
in fact each term has an $x^3$ in it

anonymous · Answer

would it make more sense that the multiplicity is 3 if i wrote 
$$(x-0)^3(x+1)^2$$?

anonymous · Answer

maybe that makes it look like all the other examples, but do not write this on a test paper or your teacher will think you are daft. just write $x^3(x+1)^2$

anonymous · Answer

No I could visualize it.

anonymous · Answer

lol, what's a daft?

anonymous · Answer

Thanks for all your help!