A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication operations. It can have one or more terms, with each term containing a variable raised to a non-negative integer power.
The degree of a polynomial is the highest exponent that appears on any variable in the expression. For example, in the polynomial 3x^4 + 2x^2 + 7, the degree is 4.
To determine the degree of a polynomial, you can look at the exponents on all the variables in the expression and find the highest one. If there is only one variable, then the highest exponent is the degree. If there are multiple variables, you need to find the highest degree among all the variables.
There are three types of polynomials based on degree: linear polynomials with a degree of 1, quadratic polynomials with a degree of 2, and cubic polynomials with a degree of 3. Polynomials with degrees higher than 3 are called higher-degree polynomials.
To graph a polynomial function, you can plot points by substituting different values for the variable in the expression and then connecting the points with a smooth curve. The degree of the polynomial will determine the general shape of the graph. You can also use the leading coefficient and constant term to determine the end behavior of the graph.