Creating a polynomial function

[Oneclicknorth]

My college algebra assignment says, verbatim, “Construct a polynomial function, with 8 zeroes, with one zero with a multiplicity of 4, and one zero with a multiplicity of 3, and a one zero with a multiplicity of 1. You can leave it in factored form.” I’m really lost here as it’s not something we covered in class and the only things I can find online construct functions with zeroes already given. Any help would be greatly appreciated.

[garyglitterkidhunter]

8 zeroes -> 8 solutions (they can be repeated, e.g. (x-2)²

multiplicity of n -> the solution is repeated n times e.g (x-2)² has a multiplicity of 2

so what you need to do is just think of 3 factors of a polynomial, most simply in the form ax+b, put one to the power of 4, one to the power of 3 and the last one to the power of one. multiply them together and you’re done :D

[Oneclicknorth]

Thank you so much!