Understanding Polynomials in Algebra

Understanding Polynomials in Algebra Polynomials are algebraic expressions that include real numbers and variables. Division and square roots cannot be involved in the variables. The variables can only include addition, subtraction and multiplication. Polynomials contain more than one term. Polynomials are the sums of monomials. A monomial has one term: 5y or -8x2  or 3.A binomial has two terms: -3x2  2, or 9y - 2y2A trinomial has 3 terms: -3x2  2 3x, or 9y - 2y2  y The degree of the term is the exponent of the variable: 3x2  has a degree of 2.When the variable does not have an exponent - always understand that theres a 1 e.g.,  1x Example of Polynomial in a Equation x2  - 7x - 6   (Each part is a term and x2  is referred to as the leading term.) Term Numerical Coefficient x2-7x-6 1 -7 -6 8x2 3x -2 Polynomial 8x-3 7y -2 NOT a Polynomial The exponent is negative. 9x2 8x -2/3 NOT a Polynomial Cannot have division. 7xy Monomial Polynomials are usually written in decreasing order of terms. The largest term or the term with the highest exponent in the polynomial is usually written first. The first term in a polynomial is called a leading term. When a term contains an exponent, it tells you the degree of the term. Heres an example of a three term polynomial: 6x2  - 4xy 2xy - This three term polynomial has a leading term to the second degree. It is called a second degree polynomial and often referred to as a trinomial.9x5  - 2x 3x4  - 2  - This 4 term polynomial has a leading term to the fifth degree and a term to the fourth degree. It is called a fifth degree polynomial.3x3  - This is a one term algebraic expression which is actually referred to as a monomial. One thing you will do when solving polynomials is combine like terms. Like  terms: 6x 3x - 3x NOT  like terms: 6xy 2x - 4 The first two terms are like and they can be combined: 5x2  2x2  - 3 Thus: 10x4  - 3 Now youre ready to start adding polynomials.