Polynomials

# Polynomials - Term A term is a number variable or the...

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A term is a number, variable or the product of a number and variable(s). Examples of terms are , z. Coefficient A coefficient is the numeric factor of your term. Here are the coefficients of the terms listed above: Term Coefficient 3 5 2 z 1 Constant Term A constant term is a term that contains only a number . In other words, there is no variable in a constant term. Examples of constant terms are 4, 100, and -5.
Standard Form of a Polynomial where n is a non-negative integer. is called the leading coefficient. is a constant. In other words, a polynomial is a finite sum of terms where the exponents on the variables are non-negative integers. Note that the terms are separated by +'s and -'s. An example of a polynomial expression is . Degree of a Term The degree of a term is the sum of the exponents on the variables contained in the term. For example, the degree of the term would be 1 + 1 = 2. The exponent on a is 1 and on b is 1 and the sum of the exponents is 2. The degree of the term would be 3 since the only variable exponent that we have is 3. Degree of the Polynomial The degree of the polynomial is the largest degree of all its terms.

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Note that the standard form of a polynomial that is shown above is written in descending order. This means that the term that has the highest degree is written first, the term with the next highest degree is written next, and so forth . Also note that a polynomial can be “missing” terms. For example, the polynomial written above starts with a degree of 5, but notice there is not a term that has an exponent of 4. That means the coefficient on it is 0, so we do not write it. Some Types of Polynomials Type Definition Example Monomial A polynomial with one term 5 x Binomial A polynomial with two terms 5 x - 10 Trinomial A polynomial with three terms Example 1 : Find the degree of the polynomial and indicate whether the
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## This note was uploaded on 02/18/2011 for the course MATH 101 taught by Professor Kindle during the Spring '11 term at South Texas College.

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Polynomials - Term A term is a number variable or the...

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