Warm Up

1) Create the following:

2) Create a Monomial, Binomial, and Trinomial

3) Find the Degree of the following a) 5x - 10 b) 6x2 + 3x - 1

4) Find the Degree and put in Standard Form: 5x5 + 3x - 7 + 4x2 + 3x4 – 1

5) Find the sum/difference: a) (9x4 + 8y + 12) – (3y2 – 7y + 2) b) ( 6x3 + 5x +11) + ( 3x3

+7x +8)

Constant

Linear Equation

Quadratic Equation

Cubic Equation

MULTIPLYING A MONOMIAL BY A

POLYNOMIAL

Review

How would you multiply 3(5x – 1) ?

Can we classify these polynomials?

Multiplying a MONOMIAL and a POLYNOMIAL Two things to remember:

1. Use the DISTRIBUTIVE PROPERTY!

2. When multiplying variables, ADD the exponents.

Example:

Examples:

You try:

Examples:

You try:

Examples:

What is different here?

You try:

Examples:

You want to find the area of the classroom. Your teacher tells you that the length is 5 feet less than twice the width. Write a single polynomial to express the area of the room.

You try:

A rectangular garden is 2x + 3 units long and 3x units wide.

A) Draw a model of the garden. B) Find the area of the garden.

Hands up, pair up

Walk around the room, high-fiving your classmates. When I say “pair up,” the person that you are high-fiving becomes your partner. Sit down together and wait quietly for the next instructions.

Partner Ticket Out

Simplify the following:

1.

2.

Homework

1.5 Study Guide Worksheet

MULTIPLYING BINOMIALS

January 31st, 2013

Warm Up

1. Multiply:

2. Multiply:

3. Simplify:

4. Find the area of the rectangle:

Summarize

What types of polynomials have we already multiplied?

What property did we use to multiply them?

Can we classify these 2 polynomials?

(2x + 3)(5x + 8)

Multiplying a BINOMIAL and a BINOMIAL Guess what: we STILL use the

DISTRIBUTIVE PROPERTY.

But we also have some special tricks to make distributing easier:FOILBox Method

FOIL

FOIL is an acronym that can help you multiply two binomials.

F – First O – Outside I – Inside L – Last

Let’s see how it works…

(y + 3)(y + 7)

Examples:

(2x + 3)(5x + 8)

Examples:

(2x – 1)(-4x + 4)

You try:

(8x + 1)(x – 3)

You try:

(5x – 3)(10x – 2)

Why is FOIL the same as the Distributive Property?

Box Method

The box method is more visual and can help you make sure that you have not missed multiplying any terms.

Box Method Draw a box and

write one binomial on the top and the other on the bottom.

Multiply each pair of terms.

Your answer is on the inside of the box. Combine like terms to write your final answer.

Example: (3x – 5)(5x + 2)

Example:

(7p – 2)(3p – 4)

Example:

(2a – 3b)(2a + 4b)

You try:

(6p – 4)(p + 10)

You try:

(p – 3)(4p – 7)

Why is the Box Method the same as the Distributive Property?

A Binomial SQUARED

What does it mean to SQUARE a number?

How could we simplify the expression

(4x + 1)2 ?

You try:

Use either method to simplify the following:

(2x – 3)2

Writing assignment

Tell whether you prefer to multiply binomials using the FOIL method or the Box method. Explain why you prefer that method in 2-3 sentences.

Practice Time

Cut the DARK squares apart. Multiply each pair of binomials and

match your answer to another square. When you think you have matched all of

the squares, let me know and I will come check your work. If it is correct, I will bring you paper and glue to glue down your puzzle.

Homework

Quotable puzzle – you must show your work!

MULTIPLYING HIGHER ORDER POLYNOMIALS

February 1st, 2013

Warm Up

1. Find the area of the rectangle below:

2. Find the area of a SQUARE with side length (x + 3)

Summarize

What type of polynomials have we multiplied so far?

Can we classify the polynomials below?

(3x + 7)(2x2 – x + 5)

How can we multiply them?

(3x + 7)(2x2 – x + 5)

Example:

(r – 2)(3r2 + 4r – 1)

Example:

(4ab – 2a + 3)(a + b)

You try:

(5x + 2)(3x2 – 8x + 10)

You try:

Find the area of the rectangle below:

Write your own

Create 3 problems for your partner to simplify:

1. MONOMIAL times a BINOMIAL

2. BINOMIAL times a BINOMIAL

3. BINOMIAL times a TRINOMIAL

Instructions

Now on a separate sheet, you should simplify each expression.

Once you both are finished simplifying your own expression, exchange the problems (without the work) with your partner.

Simplify your partners expressions then exchange back and check each others’ work.

Put it all together

Simplify: 3a(a2 – 4) + 5a2(2a + 10)

You try!

Simplify: -4b(2b + 1) – 8(b2 + 2b – 2)

Simplify:

x2(x + 1) + 5x(x – 3) – 4(x + 10)

STOP: MULTIPLY!!!Multiplication practice

Around the World I will assign your group and tell you where to

begin. Lift up the flap and simplify the expression

underneath. Look for your answer somewhere else around the room and go there to complete the next problem.

The problems form a circuit. If you have done everything correctly, you should end up where you begin.

Be sure to show your work for every problem. This is how you will earn your QUIZ grade.

Ticket Out

On a separate sheet of paper, simplify each of the following:

1. (8x – 2)2

2. (5x + 6)(x2 – 2x + 5)

3. Write 3-5 sentences explaining to your friend how to multiply polynomials.

Homework

Workbook p. 232 (#35-41)