Algebra II: Chapter 5 Part 1 (5-1:5-4) Operations with Polynomials

Section 5-1 Part 1: Monomials

A _________________________ is an expression that is a variable, a number, or the product of one or more

variables and a number.

___________________________ ___________________________________

________________________ are monomials that contain NO ___________________, like 23 and -1.

The numerical factor of a monomial is called the ___________________________. For example, the

________________________ of -6m is ________.

The ____________________ of a monomial is the sum of the exponents of its variables. For example, the

degree of 12���� is __________________. The degree of a constant is ______________.

A ____________________ is an expression of the form ________________.

Negative exponents are a way of expressing the _______________________________________ of a number.

For example, �

� can be written as ______________.

To __________________________ an expression with powers means to write it without __________________

or _____________________________________________________.

This example suggests that when you multiply two monomials with the same base, you ___________________

the exponents.

Similarly, when dividing two monomials with the same base, you ______________________ the exponents.

Summary of the Properties of Powers:

Property Example

1) Power of a Power:

2) Power of a Product:

3) Power of a Quotient:

HW: 5-1 Part 1

Section 5-1: Part 2 – Scientific Notation

The form that we usually use to write numbers is called ________________________________________. A

number is in _______________________________________ if it is in the form ________________________,

where ______________________ and n is an ___________________. Scientific notation is used to express

very ______________ or very __________________ numbers.

We can use the properties of _________________ to multiply and divide numbers in scientific notation.

HW: Part 2

Algebra II: Chapter 5 Part 1 (5-1:5-4) Operations with Polynomials

Section 5-2: Polynomials

A _______________________ is a monomial or a _____________ of monomials.

The monomials that make up a polynomial are called the _________________ of the polynomial.

The terms of a polynomial are called “like terms” if they have:

1) The same ___________________

2) The same ___________________

Ex. 1: Which of the following are like terms: 5��, 2�, 6�, 3�, 8�, 4��, 2��

A _______________________ has three unlike terms. A __________________________ has two unlike terms.

The _____________________ of a polynomial is the ____________________ of the monomial with the

greatest degree.

To ________________________ a polynomial means to perform the operations indicated and then

______________________ the like terms.

When _________________________________ polynomials, use the _________________________ Property.

When multiplying _____________________________, use the ___________________ method.

HW:

Algebra II: Chapter 5 Part 1 (5-1:5-4) Operations with Polynomials

Section 5-3: Dividing Polynomials

When dividing a polynomial by another polynomial, we use LONG DIVISION.

Let’s practice a long division problem without the calculator.

Divide: ����

��

HW:

Algebra II: Chapter 5 Part 1 (5-1:5-4) Operations with Polynomials

Section 5-4 Part 1: Factoring by Greatest Common Factor

Factoring polynomials is just like factoring numbers.

Ex. Find the prime factorization of 72.

Just as numbers are factored into the product of prime numbers, polynomials are factored into the product of

other polynomials.

Step 1: ALWAYS look for a _______________________________________ first.

HW:

5.4 Part II: Factoring Trinomials

To factor a trinomial of the form ��� � �� � �, our goal is to FOIL in ___________________________.

Factor the following:

Ex. 1:

Ex. 2:

Ex. 3:

Ex. 4:

Ex. 5:

Ex. 6:

Ex. 7:

HW Part 2: Factor the following:

5.4 Part III: Special Polynomials

The Difference of Two Squares: ��� � �� ___________________________________________.

Ex. 1: Factor �� � 16

Ex. 2: Factor 25�� � 49��

Ex. 3: Factor 36�� � 100��.

The Difference of Two Cubes: ��� � �� ________________________________________________.

Ex. 4: Factor �� � 27

Ex. 5: Factor 64�� � 1

The Sum of Two Cubes: ��� � �� _________________________________________________.

Ex. 6: Factor �� � 27

Ex. 7: Factor 27�� � 1000

HW: Factor completely.

1)

2)

5.4 Part IV – Simplifying Quotients by Factoring

In section 5.3 we simplified quotients using long division. Sometimes we can simplify by factoring.

HW Part IV: