If f and g are two polynomials of degree 3 and 4 respectively, then what is the degree of f – g.Select an answerA1B3C4DCannot be determined

To determine the degree of the polynomial $f - g$, where $f$ is a polynomial of degree 3 and $g$ is a polynomial of degree 4, we can analyze the degrees involved:

1. Understand Polynomial Degrees:

   • The degree of a polynomial is the highest power of the variable in the polynomial.
   • The degree of $f$, which is a polynomial of degree 3, is expressed as $\text{deg}(f) = 3$.
   • The degree of $g$, which is a polynomial of degree 4, is expressed as $\text{deg}(g) = 4$.

2. Subtraction of Polynomials:

   • When subtracting two polynomials, the degree of the resulting polynomial is determined by the polynomial with the highest degree, unless the leading coefficients subtract to zero.
   • In this case, since $\text{deg}(g) = 4$ is greater than $\text{deg}(f) = 3$, the resultant polynomial $f - g$ will be at least degree 4 unless the leading term of $f$ matches the leading term of $g$ exactly in a way that cancels the highest degree term.

3. Conclusion:

   • Assuming typical cases where no specific cancellation occurs (which is generally the case unless otherwise specified), the degree of $f - g$ is predominantly determined by $g$.

Final Answer

The degree of $f - g$ is $4$. Therefore, the answer is C: 4.