Question

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. f(x) = -13x^5 - 4x^4 - 1 Degree: 5; leading coefficient: -13 Degree: -13; leading coefficient: 5 Degree: 9; leading coefficient: -13 Not a polynomial function

Answer 1

By definition, a polynomial is an expression with more than one term. That is a monomial. We have names for 2-termed polynomials (binomials) and 3-termed polynomials (trinomials), but that's where the naming stops and they all are called polynomials after that. Our degree is the same as the highest exponent. So our degree is a fifth degree. The leading coefficient is the number that starts out the whole polynomial AS LONG AS IT IS IN STANDARD FORM. If our polynomial started with the -4x^4, our leading coefficient would NOT be -4 since the highest degree'd term will always come first in standard form. Your choice for your answer is the first one given. Degree: 5 Leading Coefficient: -13.