Vocabulary: What are the parts that make up a polynomial?
A polynomial is made up of the sum of one or more terms. Each term consists of a coefficient, which is a known positive or negative number or constant, multiplied by a number of variables, each raised to a non-negative integral power.
-2x^sup2;yz is a term (and a polynomial)
while
42y1/2 is not a term of a polynomial, because the power (1/2) is not an integer.
-2x²yz is a term (and a polynomial)
A polynomial is a mathematical expression that consists of variables (letters that represent numbers) and coefficients (numbers that multiply the variables). The parts that make up a polynomial are called terms. Each term in a polynomial can be further broken down into three components: the coefficient, the variable, and the exponent.
1. Coefficient: The coefficient is the number that multiplies the variable in a term. For example, in the term 3x, the coefficient is 3. If there is no explicit coefficient written, it is assumed to be 1. In the term x^2, the coefficient is 1.
2. Variable: The variable is the letter that represents an unknown number in a term. Common variables include x, y, and z. Variables are raised to various exponents, which determines their degree. For instance, in the term 2x^3, the variable is x.
3. Exponent: The exponent represents the power to which the variable is raised. It is written as a superscript (small number placed above and to the right of the variable). The exponent indicates how many times the variable is multiplied by itself. In the term 4x^2, the exponent is 2.
Combining these parts, you can form various terms in a polynomial. For example, in the polynomial 3x^2 + 5xy - 2, there are three terms: 3x^2, 5xy, and -2. Each term consists of a coefficient, a variable (or variables), and an exponent (if applicable).