A variable is a symbol that denotes a numerical
quantity. Variables are alphabetic characters. Algebra utilizes the
concept of a variable to generalize mathematical concepts to a particular
group of numbers.
The number that the variable represents is called its value.
A constant is a symbol that represents a definite
mathematical quantity.
e.g., 3, 4.9, 2/3, etc. Symbols such as P and e are also constants,
approximately denoting the values 3.14 and 2.718 respectively.
A term is a product with an unspecified number of
factors, where the factors are variables or constants. The variables of a
term are called literal factors, and the constants the numerical
coefficient (or simply coefficient), of the term. Terms that have the same
literal factors which differ only in their numerical coefficients are
called similar terms.
e.g., 3xy and 2xy are similar terms
An algebraic expression is a mathematical statement
that may use constants and variables. E.g. 5x + 2 Denny weighs 70
kilograms, and Diana weighs k kilograms. The combined weight in kilograms
of these two people is the sum of their weights, which is 70 + k.
By applying the distributive property, two or more similar terms can be
combined into one term. The new term has the same literal factors as the
similar terms, but its coefficient is the sum of the coefficients of the
similar terms. This process is known as combining similar terms. 3xy + 2xy = 5xy
A monomial is a term containing variables with only
nonnegative integers as exponents.
e.g., 4x, 5x2y.
An expression with two terms is a binomial; with three terms is a
trinomial. A polynomial has more than one term.
The degree of the polynomial is the highest power of
the variable in the terms.
The general form of a polynomial p(x) is:
Example
1. If (x + 1)2 = 100, which of the following could be the value of x -
4?
(A) -5
(B) 4 (C)-15 (D) 15 (E) None of
these
Solution: (x + 1)2 = 100 Þ x + 1 = ± 10
(i) x + 1 = 10 Þ x = 9 and x - 4 =
5
(ii) x + 1 = -10 Þ x = -11 and x - 4 =
-15
Hence, (C) is the
best choice.
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