POLYNOMIALS REVIEWObjectives: Add, Subtract, and Multiply Polynomials

Which is equivalent to x8?

a. (x3)(x5)b. (x3)5

c. (3x)(5x)d. (x2)(x4)/x21

STANDARDIZED TEST PRACTICE

REVIEW

Write an example of the 5 monomial rules. Product Rule Quotient Rule Power to a Power Rule Zero Exponent Rule Negative Exponent Rule.

Give the problem to your neighbor to simplify.

Check each other’s answers

CLASS WORK

Monomial Rules

POLYNOMIALS IN SCIENCEScientist can use algebraic expressions to summarize the possible outcomesIn genetic breeding. Certain traits result from the pairing of two genes, oneFrom the female parent and one from the male parent. See the example below.

WHAT IS A POLYNOMIAL?

A polynomial is a monomial or sum of monomials

Examples: Non Examples:

AM I A POLYNOMIAL?

4 3 3221

7

9 3

x y x

x

UNDER WHAT CONDITIONS CAN POLYNOMIALS BE ADDED OR SUBTRACTED

example 1

2 2(4 3 ) ( 2 1)x x x x

UNDER WHAT CONDITIONS CAN POLYNOMIALS BE ADDED OR SUBTRACTED

example 2

3 2 2 3 4(4 3 10 ) (8 2 )x x x x x x x

NOW YOU TRY.

Create 3 of your own practice problems. Each problem has to have an answer with at

least 3 different terms. Pass the problems your neighbor to

complete. Give them back to be corrected Each pair has to turn in 6 complete problems.

YOU TRY:

1. (3r + s) – (r – s) – (r + 3s)

2. (-12y – 6y2) + (-7y + 6y2)

3. (10x2 – 3xy + 4y2) – (3x2 + 5xy)

4. (c2 – 6cd – 2d2) + (7c2 – cd + 8d2)

5. (4x2 – 3y2 + 5xy) – (8xy + 6x2 + 3y2)

YOU TRY: ANSWERS

1. (3r + s) – (r – s) – (r + 3s)

2. (-12y – 6y2) + (-7y + 6y2)

3. (10x2 – 3xy + 4y2) – (3x2 + 5xy)

4. (c2 – 6cd – 2d2) + (7c2 – cd + 8d2)

5. (4x2 – 3y2 + 5xy) – (8xy + 6x2 + 3y2)

WHICH OPERATION?

Addition/subtraction Multiplication

ONE PROBLEM … 3 METHODS

2(4 5)( 2)x x

ONE PROBLEM … 3 METHODS

2(4 5)( 2)x x

ONE PROBLEM … 3 METHODS

2(4 5)( 2)x x

ROUND ROBINIn groups of three.

ROUND ROBIN

1. (3r + s)(r – s) FOIL

2. (-12y – 6y2)(-7y + 6y2) Boxes

3. (10x2 + 4y2)(3x2 + 5) Distribute

4. (c2 – 2d2)(7c2 – 8d2) FOIL

5. (4x2 – 3y2)(8xy + 6x2 + 3y2) Boxes

6. (3x3 – 5x2 +6x)(x2 – 7) Distribute

ROUND ROBIN - ANSWERS

1. 3r2 - 2rs – s2

2. 84y2 – 30y3 – 36y4

3. 30x4 + 50x2 + 12x2y2 + 20y2

4. 7c4 – 22c2d2 + 16d4

5. 24x4 + 32x3y – 6x2y2 – 24xy3 -9y4

6. 3x5 – 5x4 – 15x3 + 35x2 – 42x

TICKET OUT THE DOOR

1.a and 1.b