Which option has degree 12 and coefficient of x^{11} equal to 0?

Correct answer: 8x^{12}-6x^{10}+1

The degree is the highest exponent with a nonzero coefficient, while the coefficient of a missing power is understood to be zero. In option A, the degree is 12, but x^11 is present with coefficient 1, so it fails the second condition. In option B, x^11 has coefficient 8 and the degree is only 11. In option C, the term x^13 is present, so the degree is 13 rather than 12. In option D, the leading term 8x^12 has a nonzero coefficient, so the degree is 12, and there is no x^11 term at all; consequently its coefficient is 0. The term −6x^10 does not affect either required condition. Therefore option D satisfies both requirements.