1. Module 14 Polynomials and Operations
Learning goal: Students will be able to perform arithmetic operations on polynomials and find factors and zeroes of polynomials.

2. 3rd Quarter Grading Unit 4(modules 14-16)
HWK – 5% (homework questions)
CWK – 25% (notes, writing folder and classwork questions)
ASMT – 50% (modules quizzes and unit 4 test)
EXSB – 20% (3rd quarter exam)

3. Cornell Notes

4. Example

5. Polynomials and Operations
You should be able to:
evaluate expressions
simplify expressions
write expressions
represent functions
You will learn how to:
classify polynomials
evaluate polynomial expressions
add, subtract, and multiply polynomials
factor polynomials
solve quadratic polynomial expressions

6. 14.1 Understanding Polynomials
Opening activity - Explore p485
Reading assignment p
Learning goal: Students will be able to perform arithmetic operations on polynomials and find factors and zeroes of polynomials.
Essential question: What are polynomial expressions and how do you simplify them?

7. 14.1 Understanding Polynomials
1.What is different about polynomials and monomials?
2. Describe how to find the degree of a monomial.
3. Describe how to find the degree of a polynomial.

8. 14.1 Understanding Polynomials
4. How many terms are in a trinomial? a monomial?
5. Why does 5xy3 have a degree of 4?
6. Classify 4n3 + 6 by degree. by number of terms.

9. Use the polynomial 8g + 1 – 4g2 to complete the following.
Write the polynomial in standard form.
What is the leading coefficient?
What is the degree of the polynomial?
Classify the polynomial by number of terms.
11. Classify the polynomial by degree.

10. 14.1 Understanding Polynomials
Writing Folder p489 #10
Homework Questions p #12-20 evens, 28, 30, 31

11. 14.2 Adding and Subtracting Polynomials
Opening activity – Explore p493
Reading assignment p
Learning goal: Students will be able to perform arithmetic operations on polynomials and find factors and zeroes of polynomials.
Essential question: How do you add and subtract polynomials?

12. 14.2 Adding and Subtracting Polynomials
1. If m3 is represented by a cube with side length m, explain how to represent m2.
2. When subtracting one polynomial from another polynomial, what must you do first?
3. What property allows you to rearrange terms?

13. 14.2 Adding and Subtracting Polynomials
4. What is being distributed in the linear expression on the left?
5. What is being distributed in the polynomial subtraction on the right?
6. Identify the sets of like terms that were combined in the expression on the left.
7. Identify the sets of like terms that were combined in the polynomial subtraction on the right.

14. 8. 5x3  2x  1  (3x3  6) 9. x  3x5  2x4  (5x5  x)
Add or subtract the polynomials.
8. 5x3  2x  1  (3x3  6) x  3x5  2x4  (5x5  x)
10. (2x2  10x  4)  (7x2  6x  2) 11. (x3  6)  (9  2x2  x3)
12. (6x4  8x  2)  (2x4  6x) (3x2  9x)  (x  2x3  4)

15. 14.2 Understanding Polynomials
Writing Folder p498 #8
Homework Problems p #15-20 evens, 23, 25, 26

16. 14.3 Multiplying Polynomials and Monomials
Opening activity – Explore p501
Reading assignment p
Learning goal: Students will be able to perform arithmetic operations on polynomials and find factors and zeroes of polynomials.
Essential question: How can you multiply polynomials by monomials?

17. 14.3 Multiplying Polynomials and Monomials
In Problem 2, why does the subtraction change to addition?
Why did the exponents in Problem 2 remain the same?
In Problem 1, how would multiplying by -3m2n3 make the answer different?
Find the product of 3x2 and -4xy3 + 12x8 -2y4?

18. 14.3 Multiplying Polynomials and Monomials
Using the compare and contrast chart, label the expressions in Exercises 5-10 as monomials or polynomials.
3nm5
5rt – 2r2
-3xy3 + 4x
5 – 6h2g 4m
10. 6e4 – 2e

19. 17. 6s3(-2s2 + 4s - 10) 18. 2p4q2(8p4q2 - 3p3q + 5p2q)
Find the product.
11. 5x(2x4y3) p(-30p3r2)
13. 11ab2(2a5b4) c3d5(-3c2d)
15. 9x2(x3 - 4x2 - 3x) mn3(3mn3 + n2 + 4mn)
17. 6s3(-2s2 + 4s - 10) p4q2(8p4q2 - 3p3q + 5p2q)

20. 14.3 Multiplying Polynomials and Monomials
Writing Folder p506 #8
Homework Problems p #10-26 evens, 27

21. 14.4 Multiplying Polynomials
Opening activity – Explore p509
Reading assignment p
Learning goal: Students will be able to perform arithmetic operations on polynomials and find factors and zeroes of polynomials.
Essential question: How can you multiply binomials and polynomials?

22. 14.4 Multiplying Polynomials
What is the final product of the binomials in Problem 1?
How many x2 tiles are in the model? x tiles? 1 tiles?
Create a model for the product (x + 4)2.
x + 4 x + 4

23. 14.4 Multiplying Polynomials
Use the procedure shown to answer each of the following.
4. Multiplication was used six times in step 1, How many times would it be used if two binomials were being multiplied?
5. In step 2, how do you know that 5x2 and -12x2 are like terms?
6. In step 3, how do you know the expression is completely simplified?

24. 7. -3x3(2x2 - 4x + 1) 8. (2x + 5) (9x2 + 6x) 9.(7x + 2) (x - 3)
Multiply the polynomials.
7. -3x3(2x2 - 4x + 1)
8. (2x + 5) (9x2 + 6x)
9.(7x + 2) (x - 3)
10. (2x3 + 6x + 8) (x2 - 5x + 1)

25. 14.4 Multiplying Polynomials
Writing Folder p514 #11
Homework Problems p # even, 23, 25-27