6-3 Polynomials Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1

Warm Up 11/09/16 Evaluate each expression for the given value of x. 1. 2x + 3; x = 2 2. x2 + 4; x = –3 Identify the coefficient in each term. 3. 4x3 4. y3 5. 2n7 6. –b4 7 13 4 1

Essential Objectives Classify polynomials and write polynomials in standard form. Evaluate polynomial expressions.

Vocabulary monomial degree of a monomial polynomial degree of a polynomial standard form of a leading coefficient quadratic cubic binomial trinomial

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.

Example: Finding the Degree of a Monomial 4p4q3 The degree is 7. Add the exponents of the variables: 4 + 3 = 7. B. 7ed The degree is 2. Add the exponents of the variables: 1+ 1 = 2. C. 3 The degree is 0. Add the exponents of the variables: 0 = 0.

Check It Out! Find the degree of each monomial. a. 1.5k2m The degree is 3. Add the exponents of the variables: 2 + 1 = 3. b. 4x The degree is 1. Add the exponents of the variables: 1 = 1. c. 2c3 The degree is 3. Add the exponents of the variables: 3 = 3.

The terms of an expression are the parts being added or subtracted. Remember!

A polynomial is a monomial or a sum/ difference of monomials. The degree of a polynomial is the degree of the term with the greatest degree.

Example: Finding the Degree of a Polynomial A. 11x7 + 3x3 11x7: degree 7 3x3: degree 3 The degree of the polynomial is the greatest degree, 7. B. :degree 3 :degree 4 –5: degree 0 The degree of the polynomial is the greatest degree, 4.

The terms of a polynomial may be written in any order The terms of a polynomial may be written in any order. However, polynomials that contain only one variable are usually written in standard form. 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.

Example 3A: Writing Polynomials in Standard Form Write the polynomial in standard form. Then give the leading coefficient. 6x – 7x5 + 4x2 + 9 = –7x5 + 4x2 + 6x + 9 –7x5 + 4x2 + 6x + 9. Standard form is The leading coefficient is –7.

A variable written without a coefficient has a coefficient of 1. Remember! y5 = 1y5

Check It Out! 16 – 4x2 + x5 + 9x3 The standard form is The leading coefficient is 1. x5 + 9x3 – 4x2 + 16.

Some polynomials have special names based on their degree and the number of terms they have. Monomial Binomial Trinomial Polynomial 4 or more 1 2 3 1 2 Constant Linear Quadratic 3 4 5 6 or more 6th,7th,degree and so on Cubic Quartic Quintic

Example 4: Classifying Polynomials A. 5n3 + 4n a cubic binomial. Degree: 3 Terms: 2 B. 4y6 – 5y3 + 2y – 9 a 6th-degree polynomial. Degree: 6 Terms: 4 C. –2x a linear monomial. Degree: 1 Terms: 1

Lesson Quiz: Part I Find the degree of each polynomial. 1. 7a3b2 – 2a4 + 4b – 15 2. 25x2 – 3x4 Write each polynomial in standard form. Then give the leading coefficient. 3. 24g3 + 10 + 7g5 – g2 4. 14 – x4 + 3x2

Lesson Quiz: Part II Classify each polynomial according to its degree and number of terms. 5. 18x2 – 12x + 5 6. 2x4 – 1