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Algebraic Expressions and Polynomials

# 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.

consider

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.

Example 1

Identify each term of the polynomial:

The polynomial in example one consists of three terms:

, and

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.

Example 2

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.

Example 3

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.

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