Final answer:
Subtracting two polynomials of degree 4 can result in a polynomial of degree 3 if the leading terms cancel each other out.
Step-by-step explanation:
It is indeed possible to subtract two polynomials, each of degree 4, and have the difference be a polynomial of degree 3. This is true because polynomial subtraction is done by combining like terms. If the leading term (the term with the highest exponent) in both polynomials is the same and they have opposite signs, they will cancel each other out during subtraction. For example, if we have two polynomials P(x) = x^4 + 2x^3 + x^2 + x + 1 and Q(x) = x^4 - 3x^3 + 4x + 5, subtracting Q from P yields R(x) = P(x) - Q(x) = (2x^3 + x^2 + x + 1) - (-3x^3 + 4x + 5), which results in R(x) = 5x^3 + x^2 - 3x - 4, a polynomial of degree 3.