**Monomials**- A monomial is a term of the form
*axm*, where*a*is a constant and*m*is a whole number

- A monomial is a term of the form
**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

.

- The

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

- If

**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.

- Step 1. Multiply the
**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)

**Binomial Squares Pattern**- If
*a*,*b*are real numbers,

- If

**Product of Conjugates Pattern**- If
*a*,*b*are real numbers, - (
*a*−*b*)(*a*+*b*)=*a*^{2}−*b*^{2} - The product is called a difference of squares.

- If
**To multiply conjugates:****square the first term square the last term**write it as a difference of squares

**Quotient Property for Exponents:**

**Zero Exponent**- If
*a*is a non-zero number, then*a*0=1.

- If

**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.

- If

**Summary of Exponent Properties**- If
*a*,*b*are real numbers and*m*,*n*are whole numbers, then

- If

**Fraction Addition**- If
*a*,*b*,and*c*are numbers where*c*≠0, then

- If

**Division of a Polynomial by a Monomial**

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

**Property of Negative Exponents**- If
*n*is a positive integer and*a*≠0, then 1/*a*^{−n}=*a/n*

- If
**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*

- If
**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 10
*n* - between 0 and 1, the power of 10 will be 10−
*n*

- greater than 1, the power of 10 will be 10
- 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
*n*places, 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.

- Step 1. Determine the exponent,

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