Polynomials CA 10.0

Objective - To classify polynomials and write them in standard form

MONOMIALS Monomial - A single term. A group of numbers and/or variables tied together by multiplication or division but separated by addition or subtraction. single Examples: Coefficient - The number preceding a variable in a variable term.

MONOMIALS The DEGREE OF A MONOMIAL is the sum of the exponents of the variables. Example: To find the degree, ADD the exponents! 2+4=6 The degree is 6. 4 is a constant. Constants have a degree of 0 The invisible exponent is 1. The degree is 1.

POLYNOMIALS Polynomial - A variable expression consisting of many terms that can’t be combined. many Examples:

Polynomials The DEGREE OF A POLYNOMIAL is the degree of the term with the greatest degree. The highest degree is 1, so the degree of the polynomial is 1. The highest degree is 3, so the degree of the polynomial is 3. The highest degree is 4, so the degree of the polynomial is 4.

POLYNOMIALS 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 the greatest degree to the least degree.

POLYNOMIALS Re-write these in standard form:

POLYNOMIALS When a polynomial is written in standard form, the coefficient of the first term is called the LEADING COEFFICIENT. Examples: The leading coefficient is 5. The leading coefficient is 1.

POLYNOMIALS Some polynomials have special names based on their degree and the number of terms they have. DEGREE: NAME: 1 2 3 4 5 6 or more Constant Linear Quadratic Cubic Quartic Quintic 6th degree, 7th degree, …

POLYNOMIALS TERMS: NAME: 1 2 3 4 or more Monomial Binomial Trinomial

POLYNOMIALS Classify each polynomial: Degree: 3, Terms: 1 Cubic Monomial Degree: 2, Terms: 3 Quadratic Trinomial Degree: 9, Terms: 2 Ninth degree Binomial

POLYNOMIALS 25 ≠ 0, so 4 is NOT a root of A ROOT of a polynomial in one variable is a value of the variable for which the polynomial is equal to 0. Example: Tell if the number is a root of 25 ≠ 0, so 4 is NOT a root of

POLYNOMIALS 0=0, so –1 is a root of Example: Tell if the number is a root of 0=0, so –1 is a root of