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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. - PowerPoint PPT Presentation
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5.1 Monomials5.2 Polynomials
First & Last NameMarch 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.– 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)
• 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.
• 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:
• 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:
• 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:
• Power of a Quotient: and –When you have a quotient raised to a power,
raise the numerator and denominator to that power.
– Example:
1. Simplify each expression.a. 2
b.
c.
2. Simplify each expression.a.
b.
c.
a.
b.
c.
3. Simplify each expression.
• A number is in scientific notation when it is in the form , where and n is an integer.
4. Express each number in scientific notation.a. 6,380,000
b. 0.000047
• 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
5. Determine whether each expression is a polynomial. If it is a polynomial, state the degree of the polynomial.a.
b.
c.
6. Simplify.
a.
b.
7. Simplify
a.
b.
• 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
8. Simplify.
a. b.
9. Simplify.
a. b.
10. Find
Exit SlipSimplify.1. 2.
3.
4.
5. 6.