5.1 Monomials5.2 Polynomials

First & Last NameMarch 27, 2014

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• 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.