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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 are , , ..., .
The coefficient of the polynomial is , , …, , of the variable , , ..., , respectively.
Example:
1. Consider the polynomial .
The terms of the polynomial are , , .
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 .
The terms of the polynomial are \(9x^{3}\), \(-3x^{2}\), \(8x\) and \(2\).
The coefficient of is \(9\).
The coefficient of is \(-3\).
The coefficient of is \(8\).
And \(-2\) is the coefficient of .
Important!
Polynomial may have any finite number of terms.
\(p(x) =\) \(+\) \(+\) \(...\) \(+\)\(2x\) \(+\) \(3\).
A polynomial of one term is defined as a monomial. .
The two terms are referred to as binomial. .
And the three terms are referred to as trinomial. .
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.
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