What is the degree of the polynomial $(x^4+ax^7+bx+c)(x^3+dx^2+e)(x+f)$, where letters $a$ through $f$ are all nonzero constants?
To find the degree of a polynomial, I need to look at the highest power of the variable that appears in the polynomial when it is expanded. I don't need to expand the whole polynomial, since that would be tedious and unnecessary. I just need to focus on the terms that will produce the highest power of $x$ when multiplied together. Those terms are $ax^7$ from the first factor, $x^3$ from the second factor, and $x$ from the third factor. Multiplying these terms together, I get $ax^{11}$. This means that the highest power of $x$ in the expanded polynomial is 11, and therefore the degree of the polynomial is 11. 