Theory:

Consider a polynomial in one variable(\(x\)).
 
\(p(x) =\) \(a_{n}x^{n}\)\(a_{n-1}x^{n-1}\)\(+...\)\(a_{2}x^{2}\)\(+\)\(a_{1}x\)\(+a_{0}\)
 
The terms of the polynomial p(x) are anxn, an1xn1, ..., a0.
 
The coefficient of the polynomial p(x) is an, an1, …, a2, a1 of the variable xn, xn1, ..., x2, x respectively.
Example:
1. Consider the polynomial p(x)=ax28x+9.
 
The terms of the polynomial are ax2, 8x, 9.
 
The coefficient of \(x^{2}\) is \(a\).
 
The coefficient of \(x\) is \(-8\).
 
The coefficient of \(x^{0}\) constant is \(9\).
 
 
2. Consider the polynomial p(x)=9x33x2+8x2.
 
The terms of the polynomial are \(9x^{3}\), \(-3x^{2}\), \(8x\) and \(2\).
 
The coefficient of x3 is \(9\).
 
The coefficient of x2 is \(-3\).
 
The coefficient of x is \(8\).
 
And \(-2\) is the coefficient of x0.
Important!
Polynomial may have any finite number of terms.
 
\(p(x) =\) x199 \(+\) 4x198 \(+\) \(...\) \(+\)\(2x\) \(+\) \(3\).
 
A polynomial of one term is defined as a monomial. p(x)=8x.
 
The two terms are referred to as binomial. p(x)=9x3+3.
 
And the three terms are referred to as trinomial. p(x)=7x4+3x3+7. 
Constant polynomial: The constant polynomial is the form \(p(x) = c\), where \(c\) is the actual number. This means that it is constant for all possible values of \(x\), \(p(x) = c\). Polynomials \(p(x) = -3\), \(q(y) = 18\), \(r(z) = \frac{2}{5}\) are the examples of constant polynomial.
 
Zero polynomial: The constant polynomial \(0\) is called the zero polynomial. \(p(x)=0\) is the zero polynomial.