MHB Help Desk - Get Answers to Your Questions

[Tstuvshu]

Need help please

 

[Prove It]

Any product of (x - 1), (x + 1), (x - 2) and a constant, with some repeated linear factors, quadratic factor without any real roots, or irreducible cubic factor that has 1, -1 or 2 as its roots.

 

[HOI]

What kind of "help" do want? For one thing, there is no single answer. There are many polynomials that satisfy these conditions! The only factors must be (x- 1), (x+ 1), and (x- 2) but that is only three and for a sixth degree polynomial you need six so some factors must be repeated. That could be $(x- 1)^4(x- 2)(x+ 1)$ or $(x-1)^2(x- 2)^2(x+ 1)^2$ or any combination of exponents that add to six. Also, the product of factors can be multiplied by any non-zero constant.