find polynomial function of degree 4 with -1 as zero of multiplicity 3 and 0 as a zero of multiplicity 1

Question

ipwnbunnies · Answer

f(x) = (x+1)(x+1)(x+1)(x)
I think that is it. Ya see, -1 can be a "zero" 3 times, which means it has a multiplicity of 3. And 0 has the multiplicity of 1. 
When you multiply that out, you'll get a fourth degree polynomial because x*x*x*x = x^4

anonymous · Answer

so the answer would come out to x^4 +3x^3+3x^2

ipwnbunnies · Answer

I'm not sure, but that looks mighty tasty.

whpalmer4 · Answer

No, you're missing a bit on the expanded polynomial...

whpalmer4 · Answer

Right approach, however — just need to expand it correctly.

anonymous · Answer

aww i was just missing a one!

whpalmer4 · Answer

Uh, tell me what you think the answer is...

anonymous · Answer

x^4+3x^3+3x^2+x

whpalmer4 · Answer

and it may be "just missing a one" to you, but that makes it a completely different polynomial and set of zeros!  Instead of the zeros you were looking for, $$x^4+3x^3+3x^2=0$$has zeros at $x=0$ (multiplicity 2) and $x = -\frac{1}{2}(3\pm i\sqrt{3})$

Yes, your new answer is much improved!

anonymous · Answer

thank you :)

anonymous · Answer

I just learned about Polynomials, i didn't pay attention but gosh that looks hard.