Polynomials

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:

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

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!

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

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

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

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

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

After turning in your table, take a Factoring Flow Chart