If (k=-3), what will be the degree of ((k+3)x^6+2x^2+x-7)?

Correct answer: (2)

Substitute k=-3 into the polynomial. The coefficient of x^6 becomes k+3=-3+3=0, so the term 0x^6 disappears completely. The expression is then 2x^2+x-7. Its nonzero terms have powers 2, 1, and 0, and the highest of these powers is 2. Therefore the degree of the resulting polynomial is 2, so option A is correct.

It is important not to decide the degree from the original visible exponent 6 before evaluating its coefficient. A term with zero coefficient is absent and cannot determine the degree. The expression is not a constant because the terms 2x^2 and x remain, and it is not degree 6 because the x^6 term vanishes. Thus the substitution and removal of the zero term lead directly to degree 2.