I already posted this question and Reiny answered it, I just wanted to clarify my answer
Problem: If f(x) is a polynomial of degree 4, and g(x) is a polynomial of degree 2, then what is the degree of polynomial
f(x)-g(x)?
Reiny: so f(x) has to contain an x^4 term
and g(x) does NOT contain an x^4 term
so what happens to that x^4 term in f(x) when g(x) is subtracted from it ???
My answer: is is x^2? x^4-x^2
Trish, since subtraction only involves "like" terms, and g(x) does not contain any x^4 term, nothing can happen to the x^4 term of f(x)
so your result still contains the x^4 term , and thus is a polynomial of degree 4
To clarify your answer, you correctly identified that when subtracting a polynomial of degree 2 (g(x)) from a polynomial of degree 4 (f(x)), the resulting polynomial will still have a degree 4. This is because when subtracting polynomials, we only consider the highest degree terms.
In your case, f(x) has an x^4 term, while g(x) does not contain an x^4 term. When subtracting g(x) from f(x), the x^4 term in f(x) remains unchanged because there is no corresponding term in g(x) to subtract it. Therefore, the resulting polynomial f(x) - g(x) will still have a degree of 4, since the highest degree term does not change.
In summary, the degree of the polynomial f(x) - g(x) is 4.