1. Polynomials

2. What is a polynomial?
An expression that can have constants (like 4), variables (like x or y) and exponents (like the 2 in y2), that can be combined using addition, subtraction, multiplication and division, but:

3. 3x - 7 x2 – 12x + 20 –½ x3 5x4 –x5 + 2x2 Degree of a Polynomial
Linear =1
Quadratic =2
Cubic =3
Quartic =4
Quintic =5
3x - 7
The degree is the value of the greatest exponent of any expression in the polynomial.
To find the degree all that you have to do is find the largest exponent in the polynomial.
x2 – 12x + 20
–½ x3
5x4
–x5 + 2x2

4. Monomial, Binomial, Trinomial
Monomial =1 = 1 Term
Binomial = 2 Terms
Trinomial = = 3 Terms
2x3
X2 – 2x
–½x3 _ 4x + 1
Count the terms in the polynomial!

5. Standard Form of Polynomials
A polynomial is in standard form when its term of highest degree is first, its term of 2nd highest is 2nd etc..
x4 + 2x – 3x2 + 6
x4 – 3x2 + 2x + 6
17 – 9x2 + 6x
– 9x2 + 6x + 17
5x3 – 8x5
– 8x5 + 5x3

6. Leading Coefficient x4 + 2x – 3x2 + 6 1 Leading Coefficient
The coefficient of a polynomial's leading term. For example, 5 is the leading coefficient of 5x4 – 6x3 + 4x – 12.
x4 + 2x – 3x2 + 6
1 Leading Coefficient
17 – 9x2 + 6x
-9 Leading Coefficient
5x3 – 8x5
-8 Leading Coefficient

7. 5x3 + 8x2 + 3x - 17 3 2 1 0 Degree of Term Leading Coefficient
Degree of Polynomial
5x3 + 8x2 + 3x - 17
Degree of Term

8. Example 1: Classifying Polynomials
Rewrite each polynomial in standard form. Then identify the leading coefficient, degree, and number of terms. Name the polynomial.
A. 3 – 5x2 + 4x
B. 3x2 – 4 + 8x4
Write terms in descending order by degree.
Write terms in descending order by degree.
–5x2 + 4x + 3
8x4 + 3x2 – 4
Leading coefficient: –5
Leading coefficient: 8
Degree: 2
Degree: 4
Terms: 3
Terms: 3
Name: quadratic trinomial
Name: quartic trinomial

9. Example 2
Rewrite each polynomial in standard form. Then identify the leading coefficient, degree, and number of terms. Name the polynomial.
A. 4x – 2x2 + 2
B. –18x2 + x3 – 5 + 2x
Write terms in descending order by degree.
Write terms in descending order by degree.
–2x2 + 4x + 2
1x3– 18x2 + 2x – 5
Leading coefficient: –2
Leading coefficient: 1
Degree: 2
Degree: 3
Terms: 3
Terms: 4
Name: quadratic trinomial
Name: cubic polynomial with 4 terms

10. After turning in your table, take a Factoring Flow Chart