Which of the following is a trinomial?
c² + c + 6, c² - 16, - 8c, c³ + 4c² - 12c + 7

Solution:

To understand what a monomial is we have to define what a polynomial is.

A function p is a polynomial:

p(x) = \(a_{n}x^{n} + a_{n-1}x^{n-1} + a_{n-2}x^{n-2}+.........+ a_{1}x^{} + a_{0}\)

Where n is a non-negative integer and the numbers \(a_{0}, a_{1}, a_{2},....., a_{n}\) are real constants (called the coefficients of the polynomial).

All polynomials have domain (\(- \infty, \infty\)), \(a_{n} \neq\) 0 and n > 0, then n is called the degree of the polynomial.

Amongst the alternatives only c² + c + 6 has three terms and its degree is 2.

The rest of alternatives comprise one, or two or four terms (including the constant).

Therefore c² + c + 6 is a trinomial.