5-1 Monomials Objectives Multiply and divide monomials Use expressions written in scientific notation

Terminology Monomial: expression that is a number, a variable, or the product of a number and one or more variables Monomials cannot contain: 1) Variables in denominators 2) Variables with exponents that are negative 3) Variables under radicals

Constant: monomial that does not contain a variable Examples: 23; -1; 0; 1,256 Coefficient: the numerical factor of a monomial Example: The coefficient of -3x is -3. Degree of a monomial: sum of the exponents of its variables Example: has a degree of 11 Power: expression of the form , with x being the base, and n being the power (exponent).

Rules for Simplifying Monomials Product of Powers when the bases are the SAME and you are MULTIPLYING, ADD the exponents Quotient of Powers when the bases are the SAME and you are DIVIDING, SUBTRACT the exponents Negative Exponents -if an exponent is negative in the numerator, move it to the denominator and change the sign -if an exponent is negative in the denominator, move it to the numerator and change the sign

An expression is simplified if…. Each base only appears ONCE. There are no negative exponents. All powers with a numerical base are evaluated.

Directions: Simplify each expression. 1) 2) 3) 4)

More Rules for simplifying Power of a Power - when a power is raised to a power, multiply the exponents Power of a Product - when a product is raised to a power, distribute the power into EVERYTHING in the parenthesis Power of a Quotient - when a fraction or quotient is raised to a power, distribute the power to EVERYTHING in parenthesis, numerator AND denominator

Directions: Simplify each expression. 8) 9) 10) 11)

5-2 Polynomials Objectives Students will be able to: Add and subtract polynomials Multiply polynomials

Terminology Polynomial: monomial or sum of monomials Examples: Terms: monomials that make up a polynomial Like terms: monomials that can be combined (contain the same variables with the same exponents on those variables) Binomial: polynomial with two unlike terms Example: Trinomial: polynomial with three unlike terms

Example: What is the degree of The degree of a polynomial is the degree of the monomial with the greatest degree, meaning: 1) find the degree of each monomial comprising the polynomial 2) whichever monomial has the highest degree, that is the degree of the polynomial Example: What is the degree of What is the degree of

To simplify a polynomial expression means to perform the operations indicated and combine like terms. Directions: Simplify each expression. 1)

Multiplying Polynomials Use the distributive property. Start with the first term in the first polynomial, and then distribute it to each term in the second polynomial. Next, move to the second term in the first polynomial, and distribute it to each term in the second polynomial. Repeat this process until every term in the first polynomial has been distributed to each term in the second polynomial.