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# Polynomials

• A term is a number, a variable, or a product of numbers and variables.
• A monomial is a term in which the variables are only raised to whole number powers.
• A polynomial is a monomial or sum of monomials.
• A monomial is a polynomial with only one term.
• A binomial is a polynomial with exactly two terms.
• A trinomial is a polynomial with exactly three terms.
• Polynomials don’t, in the usual sense, have size (in the way that numbers do, that is). Sometimes, however, it’s necessary to compare the relative “sizes” of two polynomials anyway. To do that, we use the concept of degree.
• The degree of a term with just one variable is the power to which the variable gets raised. (This is 0 if there is no variable.)
• The degree of a polynomial is the largest degree of any of its terms.
• It is common two write polynomials in decending powers of the variable, or descending order. This leads to two more pieces of vocabulary.
• The leading term of a polynomial is the term with the highest degree.
• The leading coefficient is the coefficient of the leading term.
• Simplifying a polynomial requires that you combine all like terms.
• For polynomials with only one variable, “like terms” means that the power of the variable is the same. For example, 3x 5 and -2x 5 are like terms, but 2a 4 and 2a 2 are NOT.
• You CANNOT combine terms that are not “like”. For example, there is no way to add x 3 and x 2. ( x 3 + x 2 x 5 = x 2 x 3 ).
• Keep in mind that the variable in a polynomial represents a number. Every time a variable appears, it represents the SAME number. For example, if x = 2, then the polynomial x 3 - 5x 2 + x - 5 is the same as 2 3 - 5(2 2) + 2 - 5 = 8 - 20 + 2 - 5 = -15.

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