Critique the reasoning of others. Marcellus made the statement that the sum of two polynomials is al homial with degree equal to the highest power of \( x \) found in either of the original polynomials. He gave wing example \( +5 x+4)+(6 x+1)=3 x^{2}+11 x+5 \) agree with Marcellus? If not, give you counterexample to support your answer.

Marcellus's reasoning is not entirely accurate. While it’s true that the sum of two polynomials can result in a polynomial whose degree is equal to the higher degree of the two original polynomials, his example doesn’t support his claim. Instead of demonstrating that the sum retains the highest degree, it actually results in a polynomial of lower degree. For instance, consider the polynomials \( f(x) = 2x^2 + 3 \) and \( g(x) = -2x^2 + 1 \). When we sum them: \[ f(x) + g(x) = (2x^2 + 3) + (-2x^2 + 1) = 0x^2 + 4 \] The resulting polynomial is simply \( 4 \), which has a degree of \( 0 \), much lower than the degree of either \( f(x) \) or \( g(x) \). Therefore, it demonstrates that the sum can indeed lose the highest degree if the leading terms cancel each other out.