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# Algebra: Praxis I Exam

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Updated on Jul 5, 2011

This section will help in mastering algebraic equations by reviewing variables, cross multiplication, algebraic fractions, reciprocal rules, and exponents. Algebra is arithmetic using letters, called variables, in place of numbers. By using variables, the general relationships among numbers can be easier to see and understand.

### Algebra Terminology

A term of a polynomial is an expression that is composed of variables and their exponents, and coefficients. A variable is a letter that represents an unknown number. Variables are frequently used in equations, in formulas, and in mathematical rules to help illustrate numerical relationships. When a number is placed next to a variable, indicating multiplication, the number is said to be the coefficient of the variable.

 Examples 8c 8 is the coefficient to the variable c. 6ab 6 is the coefficient to both variables, a and b.

#### Three Kinds of Polynomials

• Monomials are single terms that are composed of variables and their exponents and a positive or negative coefficient. The following are examples of monomials: x, 5x, –6y3, 10x2y, 7, 0.
• Binomials are two nonlike monomial terms separated by + or – signs. The following are examples of binomials: x + 2, 3x2 – 5x, –3xy2 + 2xy.
• Trinomials are three nonlike monomial terms separated by + or – signs. The following are examples of trinomials: x2 + 2x – 1, 3x2 – 5x + 4, –3xy2 + 2xy – 6x.
• Monomials, binomials, and trinomials are all examples of polynomials, but we usually reserve the word polynomial for expressions formed by more than three terms.
• The degree of a polynomial is the largest sum of the terms' exponents.
##### Examples
• The degree of the trinomial x2 + 2x – 1 is 2, because the x2 term has the highest exponent of 2.
• The degree of the binomial x + 2 is 1, because the x term has the highest exponent of 1.
• The degree of the binomial –3x4y2 + 2xy is 6, because the x4y2 term has the highest exponent sum of 6.