GED Mathematical Reasoning: Introduction To Polynomials
- The prefix “poly” means “many” so it makes sense that a polynomial is a string of one or more terms being added or subtracted.
- A polynomial may contain many more than three terms, but we only have special names for those having one, two or three terms.
A polynomial containing only one term is called a “monomial.” For example: and
A polynomial containing two terms is called a “binomial.” For example: and
A polynomial containing three terms is called a “trinomial.” For example:
- The number in front of the variable part is called “coefficient” and every term contains a coefficient.
The coefficient of the first term is 7
The coefficient of the second term is 1
The coefficient of the third term, even though there appears to be no variable part, is -10
- When it comes to polynomials, the sign preceding a term goes with the term. What I mean is: If the sign is addition, the term is positive. If the sign is subtraction, the term is negative.
- A term that appears to have no variable part is called a “constant” term since there is no variable to make it vary – meaning it will always remain the same. For example, -10 in
- The degree of a polynomial containing only one variable is equal to the largest exponent.
Identify each term of the polynomial:
The polynomial in example one consists of three terms:
Notice that we state the middle term to be negative, since there is a subtraction sign preceding . This is because we can rewrite subtraction using the idea of “adding the opposite,” which makes the term negative.
Classify the polynomial in Example 1 as a monomial, binomial or trinomial.
Since the polynomial in example one has three terms, it is classified as a trinomial.
State the degree of the polynomial:
This polynomial contains 4 terms: -14 “x” cubed, -10 “x” squared, 9 “x” and -5. The coefficients in this polynomial are: -14, -10, 9, and -5. And the constant term is: -5.
The degree of a polynomial containing only one variable is equal to the largest exponent. The polynomial shown in example 3 involves only one variable, which is “x,” and the largest power of “x” is 3. Therefore, the degree of the polynomial is 3.