What is the degree of ((x^2+x+1)(x^5−x^4+x^3)−x^7)?

Correct answer: 5

The governing concept is that the degree must be determined after all like terms are combined; a leading term may cancel. Expand the product in three parts: x^2(x^5−x^4+x^3)=x^7−x^6+x^5; x(x^5−x^4+x^3)=x^6−x^5+x^4; and 1(x^5−x^4+x^3)=x^5−x^4+x^3. Adding these gives x^7+x^5+x^3 because the x^6 and x^4 terms cancel. The expression then subtracts x^7, leaving x^5+x^3. The highest nonzero exponent is 5, so option C is correct. Option A incorrectly counts the cancelled x^7 term, while options B and D overlook the actual surviving highest power.