Answer: the option C. c) 9x⁴– x³– ...
Explanation:
1) A polynomial of one variable is an expression of the kind:
[tex] a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0 [/tex]
2) The order of the polynomial is the highest exponent of the variable, this is n
3) When the expression has one term it is called a monomial, when the expression has two terms it is called a binomial, when the expression has 3 terms it is called a trinomial.
Usually expressions of that kind with two or more terms are referred as polynomial, but one term is referred as monomial.
4) For the given expressions you have:
a) 5x⁴: it is a monomial (one term), which is usually not referred as polynomial properly.
b) x⁵ – 6x⁴ + 14x³ + x²: it is a polynomial with degree 5 (the highest power).
c) 9x⁴– x³– ... : altough the expression is incomplete, assuming that the next terms are monomials with degree less than 4, then this is a polynomial with degree 4, and is the right answer choice.
d) 2x⁴ – 6x⁴: since both terms have the same power, they can be simplified into one term, - 4x⁴, and it is a monomial.
