# Key Concepts

#### 6.1 Add and Subtract Polynomials

• Monomials
• A monomial is a term of the form axm, where a is a constant and m is a whole number
• Polynomials
• polynomial—A monomial, or two or more monomials combined by addition or subtraction is a polynomial.
• monomial—A polynomial with exactly one term is called a monomial.
• binomial—A polynomial with exactly two terms is called a binomial.
• trinomial—A polynomial with exactly three terms is called a trinomial.
• Degree of a Polynomial
• The degree of a term is the sum of the exponents of its variables.
• The degree of a constant is 0.
• The degree of a polynomial is the highest degree of all its terms
.

#### 6.2 Use Multiplication Properties of Exponents

• Exponential Notation
• Properties of Exponents
• If a,b are real numbers and m,n are whole numbers, then

#### 6.3 Multiply Polynomials

• FOIL Method for Multiplying Two Binomials—To multiply two binomials:
• Step 1. Multiply the First terms.
• Step 2. Multiply the Outer terms.
• Step 3. Multiply the Inner terms.
• Step 4. Multiply the Last terms.
• Multiplying Two Binomials—To multiply binomials, use the:
• Distributive Property (Example 6.34)
• FOIL Method (Example 6.39)
• Vertical Method (Example 6.44)
• Multiplying a Trinomial by a Binomial—To multiply a trinomial by a binomial, use the:
• Distributive Property (Example 6.45)
• Vertical Method (Example 6.46)

#### 6.4 Special Products

• Binomial Squares Pattern
• If a,b are real numbers,
• Product of Conjugates Pattern
• If a,b are real numbers,
• (ab)(a+b)=a2b2
• The product is called a difference of squares.
• To multiply conjugates:
• square the first term square the last term write it as a difference of squares

#### 6.5 Divide Monomials

• Quotient Property for Exponents:
• Zero Exponent
• If a is a non-zero number, then a0=1.
• Quotient to a Power Property for Exponents:
• If a and b are real numbers, b≠0, and m is a counting number, then:
(ab)m=ambm
• To raise a fraction to a power, raise the numerator and denominator to that power.
• Summary of Exponent Properties
• If a,b are real numbers and m,n are whole numbers, then

#### 6.6 Divide Polynomials

• If a,b,andc are numbers where c≠0, then

Division of a Polynomial by a Monomial

• To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.

#### 6.7 Integer Exponents and Scientific Notation

• Property of Negative Exponents
• If n is a positive integer and a≠0, then 1/an=a/n
• Quotient to a Negative Exponent
• If a,b are real numbers, b≠0 and n is an integer , then (a/b)−n=(b/a)n
• To convert a decimal to scientific notation:
• Step 1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
• Step 2. Count the number of decimal places, n, that the decimal point was moved.
• Step 3. Write the number as a product with a power of 10. If the original number is:
• greater than 1, the power of 10 will be 10n
• between 0 and 1, the power of 10 will be 10−n
• Step 4. Check.
• To convert scientific notation to decimal form:
• Step 1. Determine the exponent, n, on the factor 10.
• Step 2. Move the decimal nplaces, adding zeros if needed.
• If the exponent is positive, move the decimal point n places to the right.
• If the exponent is negative, move the decimal point |n| places to the left.
• Step 3. Check.