Question

Select the correct answer. Let f(x) and g(x) be polynomials as shown below:

f(x) = a + ax + a²x² + ... + aₙxⁿ
g(x) = b₀ + b₂x + b₂x² + ... + bₘxᵐ
Which of the following is true about f(x) and g(x)?
A) f(x) is a polynomial of degree n and g(x) is a polynomial of degree m.
B) f(x) and g(x) both are polynomials of the same degree.
C) f(x) may or may not be a polynomial, whereas g(x) is a polynomial.
D) f(x) and g(x) may or may not be polynomials.

Answer 1

Option A is correct; f(x) is a polynomial of degree n and g(x) is a polynomial of degree m, with the degrees determined by their highest degree terms.

Step-by-step explanation:

The question pertains to the degrees of two given polynomial functions, f(x) and g(x). Option A states that f(x) is a polynomial of degree n and g(x) is a polynomial of degree m, quite correctly. This is because polynomials are defined by their highest degree term, with degree n corresponding to the term anxn in f(x) and degree m corresponding to the term bmxm in g(x). Therefore, f(x) and g(x) have different degrees unless n happens to equal m by coincidence, debunking the other options.