Algebra - 01

Refresher

Terms, Factors, Coefficients and Expressions

A term is a number or the combination of product of numbers. Each of the numbers being multiplied is a factor of the term. Thus, the term −8xy consists of three factors: −8, x and y. In the term −8xy, xy is the literal coefficient and −8, the numerical coefficient.

Like terms have the same literal coefficient, while unlike terms have different literal coefficients. Thus, 9 x 2 y and 2 x 2 y are like terms, while 9 x 2 y and 9 x y 2 are unlike terms.

An expression consists of one or more terms. Expressions may be monomials or polynomials, which are described below.

Monomials and Polynomials

A monomial is an expression of one term, e.g. 12 x 2 . A polynomial is an expression of two or more terms. A binomial is a polynomial of two terms, while a trinomial is a polynomial of three terms. Thus the polynomial 7 x 3 + 2 is a binomial, while the polynomial 2 x 2 + 7 x − 4 is a trinomial.

Linear Polynomials

A polynomial of degreeThe degree of an expression that has not more than one variable in each term is the highest power to which that variable is raised in the expression. 1 is a linear polynomial. The general form of a linear polynomial is:

where a and b are real numbers, and a ≠ 0 .

Thus, x + 7 and 5 x − 2 are linear polynomials.

Quadratic Polynomials

A polynomial of degree 2 is a quadratic polynomial. The general form of a quadratic polynomial is:

where a and b are real numbers, and a ≠ 0 .

Thus, 7 x 2 + 2 x − 5 is a quadratic polynomial.

Cubic Polynomials

A polynomial of degree 3 is a cubic polynomial. The general form of a cubic polynomial is:

where a and b are real numbers, and a ≠ 0 .

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