# Shared Flashcard Set

## Details

+, -, x of Polynomials
Basic Concepts of Algebra-R3
17
Mathematics
03/20/2008

Term
 Polynomials in One Variable
Definition
 A polynomial in one variable is any expression of the type      anxn + an-1xn-1 + · · · + a2x2 + a1x + a0, where n is a nonnegative integer and an, . . . a0 are real numbers, called coefficients.
Term
 Term
Definition
 The parts of a polynomial separated by plus signs.
Term
Definition
 In a polynomial in one variable of the type      anxn + an-1xn-1 + · · · + a2x2 + a1x + a0, the leading coefficient is an.
Term
 Constant Term
Definition
 In a polynomial in one variable of the type      anxn + an-1xn-1 + · · · + a2x2 + a1x + a0, the constant term is a0.
Term
 Degree
Definition
 In a polynomial in one variable of the type      anxn + an-1xn-1 + · · · + a2x2 + a1x + a0, if an ≠ 0, the degree of the polynomial is n.
Term
 Descending Order
Definition
 A polynomial in one variable of the type      anxn + an-1xn-1 + · · · + a2x2 + a1x + a0 is said to be written in descending order because the exponents decrease from left to right.
Term
 Degree of a Term
Definition
 The degree of a term is the sum of the exponents of the variables in that term.
Term
 Degree of a Polynomial
Definition
 The degree of a polynomial is the degree of the term of highest degree.
Term
 monomial
Definition
 A polynomial with just one terme.g., -9y6
Term
 binomial
Definition
 A polynomial with two termse.g., x2 + 4
Term
 trinomial
Definition
 A polynomial with three termse.g., 4x2 - 4xy + 1
Term
 like terms or similar terms
Definition
 If two terms of a n expression have the same variables raised to the same powers, they are called like terms or similar terms.  We can combine, or collect, like terms using the distributive property.e.g., 3y2 + 5y2 = (3 + 5)y2                                        = 8y2
Term
 Square of a Sum
Definition
 (A + B)2 = A2 + 2AB + B2
Term
 Square of a Difference
Definition
 (A - B)2 = A2 - 2AB + B2
Term
 Product of a Sum and a Difference
Definition
 (A + B) (A - B) = A2 - B2
Term
 Product of Two Binomials
Definition
 (A + B) (C + D) = AC + AD + BC + BD
Term
 The Cube of a Sum
Definition
 (A + B)3 = A3 + 3A2B + 3AB2 + B3
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