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

Polynomials

1. 3x3+4x2-6x-10

2. 100z12+z2-4

3. 4x – 7/3

4. 7a2b4-6ab3-9/2

5. -3xyz2

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.Po

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ials

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.

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 signc. Terms can not have variables raised to negative or fractional exponents.

Polynomial

1. 2. 3. 4. 1

xx

1

3y4y

x+3 is a polynomial. The terms are x and 3. The coefficients are 1 and 3.

3x2 -2x +5 is a polynomial. The terms are 3x2, 2x,5. The coefficients are 3, -2 and 5

is NOT a polynomial because of the division by x in the third term.

3 35 2x x

x

3. Classifying Polynomials by their DEGREEThe degree of a polynomial that has only one variable is the highest power appearing in any one term.

5x3 -3x2 +4x …………. has degree 3

4x – 5x4 +3x3 +2…… has degree 4

8x ……………………….. has degree 1

7…………………………… has degree 0

the highest power

the highest power

Because 8x = 8x1

The degree of any constant nonzero term is 0

3. Classifying Polynomials by their DEGREE (cont)Sometimes polynomials have more than one variable in a term, such as 4x2y3 + 5xy2 . 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.

5x7 -3x4 +2x2 is in descending order4x4 +5x6 -3x5 is NOT in descending order:

4x2y3 = 2+3 = 5th degree

Variables are also written in alphabetical

order

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POLYNOMIAL CHART

Quick Check 1

Which expressions are polynomials?21. 5x 3 5

2. 3 2y yy

2 23. 4 3

3x x

Classify each polynomial as monomial, binomial, or trinomial.

4 34. 5 2x x 75. 4x26. 2 5 3x x

Find the degree of each polynomial.

Write each Polynomial in descending order.

5 37. 6 3 2x x 8. 5x 5 2 2 89. 3 5x y x y 10. 9

4 513. 5 4 7x x 3 4 814. 4 9 6x x x