A polynomial of degree n is an expression of the form:
[tex]ax^{n}+bx^{n-1}+cx^{n-2}+...+dx^{2}+ex+f[/tex]
where a, b, c, ...d, e, f are Real numbers, and any of them can be = 0, except a.
and the degrees, n, n-1, .... are all non-negative integers: {0, 1, 2, 3 ...}
Among our choices,
the first one,[tex]5x^{4}+ \sqrt{4x} [/tex],
does not fit the polynomial definition, so the expression is not a polynomial.
the second one, is a fifth degree polynomial
the third one, [tex]9x^{4}-x^{3}- \frac{1}{5}x [/tex] is a fourth degree polynomial.
the fourth one, [tex] 2x^{4}-6x^{4}+ \frac{14}{x}= -4x^{4}+ \frac{14}{x}[/tex] is not a polynomial
Answer: 9x4 – x3 – x/5
