Hobbies And Interests
Terms
A term in a polynomial is a number, a variable, or the product of a number and variable. In the polynomial, x + 2y + y-squared = 50; x, 26 and y-squared are all terms. A term with only a number is referred to as a constant term. In this example, 50 is a constant term.
Coefficients, Leading Coeffcients and Constant Terms
When a polynomial term contains a variable (x, y or z) and a number preceding the variable, the number before the variable is referred to as the coefficient. The coefficients of these terms, 3x, 2y or 4z, is 3, 2 and 4 respectively. There may be no visible coefficient in the case of a single-value variable (x, y or z), where the coefficient is understood to be 1. The coefficient of the first term is referred to as the "leading coefficient." In the polynomial, 4x + 3y +15 = 21, 4 and 3 are coefficients and 4 is the leading coefficient. In this example, 15 is a constant term and does not have a coefficient.
Exponents and Variables
Exponents are a notation used for repeated multiplication of the variable by itself. If the exponent of the variable or number is 2, the variable is multiplied by itself one time. For example; if the variable is 3, and the exponent is 2, the resultant product is 9 (3-squared, or 3 multiplied by 3).To illustrate the use of a variable, in the polynomial x + 3 = 7; solve for x, x is the variable.
Degree of a Polynomial
The degree of the polynomial is the value of the highest degree term the polynomial contains. For example; in the polynomial equation, x + x-squared = 10, the highest degree in this algebraic expression is 2, where 2 represents the "square" in x-squared. This polynomial is a second-degree polynomial. If the formula was x + x-cubed = 10, the polynomial is a third-degree polynomial.