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1 1.Definition – Polynomial an algebraic expression that can be written as a term or as the sum or difference of terms.

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2 1. 3x 3 +4x 2 -6x-10 2. 100z 12 +z 2 -4 3. 4x – 7/3 4. 7a 2 b 4 -6ab 3 -9/2 5. -3xyz 2 6. 45 A formal definition can be confusing, so look at the examples. Monomial: A polynomial with one term – examples 5 and 6. Binomial: A polynomial with 2 terms - Examples 3. Trinomial: A polynomial with 3 terms – example 2 and 4. A formal definition can be confusing, so look at the examples. Monomial: A polynomial with one term – examples 5 and 6. Binomial: A polynomial with 2 terms - Examples 3. Trinomial: A polynomial with 3 terms – example 2 and 4. A formal definition can be confusing, so look at the examples. Classifying Polynomials by their TERMS Monomial: A polynomial with one term – examples 5 and 6. Binomial: A polynomial with 2 terms - Examples 3. Trinomial: A polynomial with 3 terms – example 2 and 4.

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3 2. When is an algebraic expression NOT a polynomial? a. terms can not have variables in the denominator of a fraction. b. terms can not have variables under a radical sign c. Terms can not have variables raised to negative or fractional exponents. Polynomial 1. 2. 3. 4. x+3 is a polynomial. The terms are x and 3. The coefficients are 1 and 3. 3x 2 -2x +5 is a polynomial. The terms are 3x 2, 2x,5. The coefficients are 3, -2 and 5 is NOT a polynomial because of the division by x in the third term.

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3.Classifying Polynomials by their DEGREE The degree of a polynomial that has only one variable is the highest power appearing in any one term. 5x 3 -3x 2 +4x …………. has degree 3 4x – 5x 4 +3x 3 +2…… has degree 4 8x ………………………..has degree 1 7……………………………has degree 0 the highest power Because 8x = 8x 1 The degree of any constant nonzero term is 0

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3.Classifying Polynomials by their DEGREE (cont) Sometimes polynomials have more than one variable in a term, such as 4x 2 y 3 + 5xy 2. The degree is then the highest sum of the powers in any single term. For the above example, the degree would be : 4. Writing Polynomials in descending order. Working with polynomials is much easier if you get used to writing them in descending order. This simply means that the term with the highest exponent is written first, then the term with the next highest exponent, and so on. 5x 7 -3x 4 +2x 2 is in descending order 4x 4 +5x 6 -3x 5 is NOT in descending order: 4x 2 y 3 = 2+3 = 5 th degree Variables are also written in alphabetical order

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Quick Check 1 Which expressions are polynomials? Classify each polynomial as monomial, binomial, or trinomial. Find the degree of each polynomial. Write each Polynomial in descending order.

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