A polynomial is an algebraic expression of ordered addition, subtraction, and multiplication of variables, constants, and exponents. A polynomial can have more than one variable (x, y, z), constants (integers or fractions), and exponents (which can only be positive integers).
Then, let us see examples of what a polynomial is and is not:
• They are not polynomials
[tex]\frac{2}{x+2}[/tex]Because the variable cannot be in the denominator
[tex]3x^{-2}[/tex]Because the exponent is -2 and the exponents can only be 0,1,2, ..., etc.
[tex]\sqrt[]{x}=x^{\frac{1}{2}}[/tex]Because the exponent cannot be a fraction
• They are polynomials
[tex]\begin{gathered} 3x \\ x-2 \\ \frac{3}{8}x+x^2+5x^3+18x^6 \end{gathered}[/tex]According to the above, the given expression is a polynomial because it is a sum of a variable with integer and positive exponents. Also, the variable is not in the denominator of any fraction.
• Now, according to the ,number of terms, in a polynomial, there are ,3 types of polynomials,. They are ,monomial, binomial and trinomial,. For example:
[tex]\begin{gathered} 3x^2\Rightarrow\text{monomial} \\ 2x+7\Rightarrow\text{ binomial} \\ 5x+8y-4z+6w-3\Rightarrow\text{ polinomial} \end{gathered}[/tex]In this case, the given expression has two terms, and then it is a binomial.
Finally, the degree of a polynomial is the highest exponent value of any of its terms.
Therefore, the degree of the given polynomial is 4.
