A polynomial is an expression in which the variables can have only positive, whole-number exponents. \u00a0Examples of polynomials are\u00a03x7<\/span><\/sup>-12x5<\/span><\/sup>+1 or \u00a0-2x – 12.<\/p>\n In a polynomial, terms are separated by plus or minus signs. \u00a0Therefore,\u00a07x – 12 has two terms, whereas \u00a0-13x7<\/span><\/sup>yz2<\/span><\/sup> has only one.<\/p>\n Polynomials are often named by how many terms they have, as follows:<\/p>\n 7x2<\/span><\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0One term: monomial<\/p>\n 3x – 12 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Two terms: binomial<\/p>\n -4x4<\/span><\/sup> + 3x -5 \u00a0 \u00a0 Three terms: trinomial<\/p>\n A polynomial with more than three terms is just called a polynomial.<\/p>\n Consider the following monomial:<\/p>\n -11x5<\/span><\/sup><\/p>\n -11 is called the coefficient. \u00a0x is called the variable. \u00a05 is the exponent.<\/p>\n The degree of a polynomial is the highest exponent found in one of its terms. \u00a0For example, 5x3<\/span><\/sup> has degree 3. The trinomial<\/p>\n x7<\/span><\/sup> + 3x3<\/span><\/sup> – 12<\/p>\n has degree 7.<\/p>\n The constant term of a polynomial is the term with no variable attached. In 3x – 12, the constant term is -12.<\/p>\n There are two facts about polynomials that might be a little surprising:<\/p>\n Fact 1<\/span>:<\/p>\n A constant term has degree zero. \u00a0Reason: x0<\/span><\/sup>= 1 by definition. The result:<\/p>\n 3x0<\/span><\/sup> = 3(1) = 3.<\/p>\n We just write 3, but the degree of the term is still zero.<\/p>\n Fact 2<\/span>:<\/p>\n If the coefficient is not written, it is 1. \u00a0Reason: x5<\/span><\/sup> = 1x5<\/span><\/sup>.<\/p>\n There are a couple of finer points, but the above is good for a start. \u00a0Much more will be said about polynomials in future posts.<\/p>\n