Polynomials What is a polynomial An expression that
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Polynomials
What is a polynomial? An expression that can have constants (like 4), variables (like x or y) and exponents (like the 2 in y 2), that can be combined using addition, subtraction, multiplication and division, but:
Degree of a Polynomial Linear 3 x - 7 Quadratic 2 x =1 – 12 x + 20 =2 Cubic –½ x 3 =3 Quartic 4 5 x =4 Quintic –x 5 + 2 x 2 =5 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.
Monomial, Binomial, Trinomial Monomial Binomial Trinomial 3 2 x =1 2 X = 1 Term – 2 x –½x 3 _ 4 x + 1 = = 2 Terms = 3 Terms 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 2 nd highest is 2 nd etc. . x 4 + 2 x – 3 x 2 + 6 17 – 3 5 x 9 x 2 – + 6 x 5 8 x 4 x – – 2 9 x – 5 8 x 2 3 x + 2 x + 6 x + 17 + 3 5 x
Leading Coefficient The coefficient of a polynomial's leading term. For example, 5 is the leading coefficient of 5 x 4 – 6 x 3 + 4 x – 12. x 4 + 2 x – 3 x 2 + 6 1 Leading Coefficient 17 – 9 x 2 + 6 x -9 Leading Coefficient 3 5 x -8 Leading Coefficient – 5 8 x
Leading Coefficient 3 5 x 3 + Degree of Polynomial 2 8 x + 3 x - 17 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 – 5 x 2 + 4 x B. 3 x 2 – 4 + 8 x 4 Write terms in descending order by degree. – 5 x 2 + 4 x + 3 8 x 4 + 3 x 2 – 4 Leading coefficient: – 5 Leading coefficient: 8 Degree: 2 Degree: 4 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. 4 x – 2 x 2 + 2 B. – 18 x 2 + x 3 – 5 + 2 x Write terms in descending order by degree. – 2 x 2 + 4 x + 2 1 x 3– 18 x 2 + 2 x – 5 Leading coefficient: – 2 Leading coefficient: 1 Degree: 2 Degree: 3 Terms: 4 Name: quadratic trinomial Name: cubic polynomial with 4 terms
After turning in your table, take a Factoring Flow Chart
