When the expression $(2x^4+3x^3+x-14)(3x^{10}-9x^7+9x^4+30)-(x^2+5)^7$ is expanded, what is the degree of the resulting polynomial?
To find the degree of a polynomial, I need to look for the term with the highest power of x and ignore the coefficients. So, in the first part of the expression, $(2x^4+3x^3+x-14)(3x^{10}-9x^7+9x^4+30)$, I need to multiply the highest power of x in each factor, which are $x^4$ and $x^{10}$. That gives me a term of $x^{14}$, which has degree 14. In the second part of the expression, $-(x^2+5)^7$, I need to raise the highest power of x in the base, which is $x^2$, to the exponent, which is 7. That gives me a term of $x^{14}$, which also has degree 14. So, the highest power of x in the whole expression is $x^{14}$, and that means the degree of the resulting polynomial is 14.

