Name: Date:__________ Period: __________

CHAPTER 8: POLYNOMIALS AND FACTORING

Notes #7

8-1: Adding and Subtracting Polynomials

A. Describing polynomials

A ____________________ is an expression that is a number, a variable, or a product of a

number and one or more variables.

Ex:

The _____________ of a monomial is the sum of the exponents of its variables. For a

nonzero constant, the degree is ___. Zero has ____ degree.

Find the degree of each monomial.

1.) 2.) 3.)

Standard form of a polynomial means that the degrees of its monomial terms

______________ from left to right.

The ____________ of a polynomial in one variable is the same as the degree of the

monomial with the greatest exponent.

Ex:

Polynomial Degree Name Using Degree

Number of Terms

Name Using Number of

Terms

5

Write each polynomial in standard form. Then name each polynomial based on its degree and

number of its terms.

4.) 5.) 6.)

B. Adding and subtracting polynomials

You can add polynomials by adding or subtracting like terms. You can add or

subtract vertically or horizontally.

Simplify.

7.) 8.)

9.) 10.)

11.)

Notes #88-2: Multiplying and Factoring

A. Distributing a monomial

Simplify each product.

1.) 2.) 3.)

2

B. Factoring a monomial from a polynomial

Find the common factor of the terms of each polynomial.

4.) 5.) 6.)

To factor a polynomial completely, you must factor until there are no common factors

other than ____.

Factor. Distribute to check your answer.

7.) 8.)

9.) 10.)

11.) 12.)

13.) 14.)

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C. Applications to Reducing Fractions

Factor the ______________________ and _________________________ completely

Cancel common terms in the __________________________ and common factors ( )

Ex: Ex:

Simplify. (Factor first!!)

15.) 16.) 17.)

18.) 19.) 20.)

21.) 22.)

Notes #9

4

8-3: Multiplying Binomials

A. Multiplying two binomials

One way to organize multiplying two binomials is to use FOIL, which stands for:

o F

o O

o I

o L

Simplify.

1.) 2.)

3.) 4.)

5.) 6.)

B. Multiplying a trinomial and a binomial

Simplify the product.

7.) 8.)

5

8-4: Multiplying Special Cases

A. Finding the square of a binomial (___________ in disguise!)

The square of a binomial:

o

o

Find each square.

9.) 10.) 11.)

12.) 13.) 14.)

Notes #10

8-8: Factoring 4-termed Polynomials

Steps: 12x3 + 15x – 4x2 – 5

Write in standard form (descending order)

Check for a GCF

Draw a 2x2 box and fill it in with the four terms

Find the GCF for each row and each column

Write your answer as (______)(______)

FOIL to check

Factor using the Box Method. FOIL to check..

6

1.) 2.)

3.) 4.)

5.) 6.)

7.) 8.)

Simplify: ( _________________ first!!)

9.) 10.)

7

11.) 12.)

13.)

14.) 15.) 16.)

8

Notes #11:

8-5: Factoring Trinomials using the X-Box Method

Steps:

Write in descending order

Take out a GCF

Draw an X and a Box.

Fill them in like this:

Factor and Check like before

Factor and check using FOIL.

1.) 2.) 3.)

4.) 5.) 6.)

7.) 8.) 9.)

9

10.) 11.) 12.)

13.) 14.) 15.)

Simplify: (_____________ first!!)

16.) 17.)

18.) 19.)

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Notes #128-6: Factoring Trinomials of the Type ax2 + bx + c

Steps:

Write in descending order

Take out a GCF

Draw an X and a Box.

Fill them in like this:

Factor and Check with FOIL

Factor.

1.) 2.)

3.) 4.)

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Simplify:

5.) 6.)

Notes #13: Notes (below)/Group Quiz/Class work (Factoring Review)

8-7: Factoring Special Cases

A. Factoring Review and Factoring Perfect-square trinomials

Take out GCF

Factor using Box (4-terms) or X-Box (2 or 3 terms)

Check using FOIL

If the answer is the product of two identical binomials, write as (________)2

Factor.

1.) 2.) 3.)

4.) 6x2 – 54 5.) 6.)

7.)

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