It is a polynomial. Degree: 4 Leading term: $2x^4$ Constant: 2 $ G(x)=2x^4 - 4x^3 +4x^2 -4x+2$
Work Step by Step
First, we simplify: $$G(x)= 2(x-1)^2 (x^2 +1) \\ G(x)= 2(x^2 -2x +1)(x^2 +1) \\ G(x)=2x^4 - 4x^3 +4x^2 -4x+2$$ By definition, a polynomial is a function containing only terms where x is raised to a positive, integer power or constants. This is true, so we see that it is a polynomial. The degree is equal to the exponent of the term with the highest exponent, so the degree is 4. The term that has the highest degree, $2x^4$, is always the leading term. Finally, 2 is the constant.