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5.1 Monomials 5.2 Polynomials

5.1 Monomials 5.2 Polynomials. First & Last Name March 27, 2014 ______Block. A monomial is an expression that is a number, a variable, or the product of a number and one or more variables.

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5.1 Monomials 5.2 Polynomials

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  1. 5.1 Monomials5.2 Polynomials First & Last Name March 27, 2014 ______Block

  2. A monomial is an expression that is a number, a variable, or the product of a number and one or more variables. • Cannot contain variables in denominators, variables with exponents that are negative, or variables under radicals • Constants are monomials that contain no variables (ex: 23 or -1) • The numerical factor of a monomial is the coefficient of the variable (ex: In -6m, -6 is the coefficient)

  3. The degree of a monomial is the sum of the exponents of its variables (Ex: The degree of is 11.) • A power is an expression of the form • To simplify an expression containing powers means to rewrite the expression without parentheses or negative exponents.

  4. Negative Exponents: • When you have negative exponents move them to the other side of the fraction and make them positive. • Example: • Product of Powers: • When multiplying with the same base, add the exponents. • Example:

  5. Quotient of Powers: • When dividing with the same base, subtract the exponents. • Example: • Zero Power: Any nonzero number raised to the zero power is equal to 1. • Example:

  6. Power of a Power: • When you have a power raised to a power, multiply the exponents. • Example: • Power of a Product: • When you have a product raised to a power, raise each factor to that power. • Example:

  7. Power of a Quotient: and • When you have a quotient raised to a power, raise the numerator and denominator to that power. • Example:

  8. 1. Simplify each expression. • 2 c.

  9. 2. Simplify each expression. a.

  10. 3. Simplify each expression. a. b. c.

  11. A number is in scientific notation when it is in the form , where and n is an integer.

  12. 4. Express each number in scientific notation. • 6,380,000 • 0.000047

  13. A polynomial is a sum of monomials. • The monomials that make up a polynomial are called the terms of the polynomial. • The degree of a polynomial is the degree of the monomial with the greatest degree. • Example: The degree of is 2 The degree of is 3

  14. 5. Determine whether each expression is a polynomial. If it is a polynomial, state the degree of the polynomial. a. b. c.

  15. 6. Simplify. b.

  16. 7. Simplify a. b.

  17. The FOIL method is used to multiply binomials. It is an application of the Distributive property. • F: first terms • O: outer terms • I: inner terms • L: last terms

  18. 8. Simplify. a. b.

  19. 9. Simplify. a. b.

  20. 10. Find

  21. Exit Slip Simplify. 1. 2. 3. 4. 5. 6.

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