Let f (x) be a polynomial function with a zero of multiplicity of 1 at 2 and a zero of multiplicity of 2 at 1. Let g(x) be the radical function g of x equals the cube root of x minus 2

Question

Using the Factor Theorem, determine the polynomial function f (x) in expanded form. Show all necessary calculations.

Answer 1

So Payton M.,

You SHOULD know that zeros for a polynomial function are one-to-one associated with factors, and that the polynomial expression can be expressed as a product of several factors.

So, figure out what in a factor (something of form (x-a) ) where x is the variable, and a is a positive, negative, or zero number ) would make a product incorporating it become zero? How about, if the factor itself were (the value) zero?

So how can you assemble the poynomial?

"A zero of multiplicity 1 at 2" turns into the factor: (x-2) because when x=2, then the factor expression value is zero, and any product made from it is also zero.

""multiplicity of 2" means that you have TWO identical factors, and both are (x-1) [ in this case!] .

Can you please do the final multiplication of the three factors by yourself?

--Cheers, --Mr. d.