Lesson 5 2 Polynomials Objectives To classify a
Lesson 5 -2 Polynomials Objectives: • To classify a polynomial by the degree and number of terms • Add and subtract polynomials
Vocabulary A monomial is a number, a variable, or a product of numbers and variables with whole-number exponents. The degree of a monomial is the sum of the exponents of the variables. A constant has degree 0.
Monomials Find the degree of each monomial. a. 1. 5 k 2 m d. 4 p 4 q 3 b. 7 ed e. 4 x C. 3 f. 2 c 3
Vocabulary A polynomial is a monomial or a sum or difference of monomials. The degree of a polynomial is the degree of the term with the greatest degree.
Types of polynomials Degree Name Terms Name 0 Constant 1 Monomial 1 Linear 2 Binomial 2 Quadratic Trinomial 3 4 Cubic Quartic 3 4 or more 5 Quintic 6 or more 6 th, 7 th, degree and so on Polynomial
Vocabulary The standard form of a polynomial that contains one variable is written with the terms in order from greatest degree to least degree. When written in standard form, the coefficient of the first term is called the leading coefficient.
Polynomials Write the polynomial in standard form, give the leading coefficient. Then classify by degree and number of terms. – 7 x 5 + 4 x 2 + 9 y 2 + y 6 – 3 y
Polynomials Write the polynomial in standard form, give the leading coefficient. Then classify by degree and number of terms. 4 n - 5 n 3 – 2 x
Polynomials Write the polynomial in standard form, give the leading coefficient. Then classify by degree and number of terms. 16 – 4 x 2 + x 5 + 9 x 3 18 y 5 – 3 y 8 + 14 y
Adding and Subtracting Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms. Example: 12 p 3 + 11 p 2 + 8 p 3
Adding and Subtracting 5 x 2 – 6 – 3 x + 8 t 2 + 2 s 2 – 4 t 2 – s 2 10 m 2 n + 4 m 2 n – 8 m 2 n 4 z 4 – 8 + 16 z 4 + 2
Adding and Subtracting Add the following polynomials (4 m 2 + 5) + (m 2 – m + 6) (10 xy + x) + (– 3 xy + y) (5 a 3 + 3 a 2 – 6 a + 12 a 2) + (7 a 3 – 10 a)
Adding and Subtracting Subtract the following polynomials (x 3 + 4 y) – (2 x 3) (7 m 4 – 2 m 2) – (5 m 4 – 5 m 2 + 8)
Adding and Subtracting Subtract the following polynomials (– 10 x 2 – 3 x + 7) – (x 2 – 9) (9 q 2 – 3 q) – (q 2 – 5) (2 x 2 – 3 x 2 + 1) – (x 2 + x + 1)
- Slides: 14