If f(x) = -7x^4 + 3x^3 + x - 5, and g(x) is a polynomial such that the degree of f(x) + g(x) is 1, then what is the degree of g(x)?
The degree of a polynomial is the degree of its highest degree term.
Therefore, the degree of f(x) = -7x4 + 3x3 + x - 5 is 4.
For the degree of f(x) + g(x) to be 1, g(x) must have cancelled out the -7x4 and the 3x3 terms but left the x term.
So, g(x) must include a +7x4 term and a -3x3 term but no other terms larger than x (and, not just a -x term, that would
cancel out all the x-terms and leave a degree of 0).
---> the degree of g(x) must be 4.