1. Section 4.2 Adding, Subtracting and Multiplying Polynomials
Honors Algebra 2
Section 4.2
Adding, Subtracting and Multiplying Polynomials

2. Warm Up
Do the problems in Exploration 1 on page 165

3. Adding and Subtracting Polynomials
Your book has two methods. Skip the vertical method!
If you know how to do distributive property and combine like terms, you can add and subtract polynomials!!
Always write final answers in standard form.

4. #1 Add 2 𝑥 3 + 𝑥 2 −3𝑥+4 and 5 𝑥 3 −7 𝑥 2 −8 #2 Find the sum
#1 Add 2 𝑥 3 + 𝑥 2 −3𝑥+4 and 5 𝑥 3 −7 𝑥 2 −8 #2 Find the sum. 2𝑥 4 −6 𝑥 3 +9 𝑥 2 −𝑥+1 +( 𝑥 5 + 5𝑥 3 −6𝑥+2) #3 Subtract 5𝑥 3 − 2𝑥 2 +𝑥−7 from 4 𝑥 3 +2 𝑥 #4 Find the difference. 2𝑥 3 − 8𝑥 2 +4𝑥−11 −( 𝑥 4 + 4𝑥 3 −6𝑥+2)

5. Multiplying Polynomials Case#1
Monomial times Polynomial
Use distributive property!
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑥 2 (4 𝑥 4 −3 𝑥 2 +5)

7. Multiplying Polynomials Case #2
Polynomial times Polynomial For binomials, use FOIL. #1 3𝑥+5 2𝑥−7 #2 ( 𝑥 2 −8)( 𝑥 2 −2) #3 𝑦+6 2𝑦+9 #4 (𝑚−1)(𝑚+1)

8. Multiplying Polynomials
Any polynomial × Any polynomial
Count the number of terms in the first factor
Count the number of terms in the second factor
The product of the counted terms is the number of multiplications to be done.

10. 𝑥−3 𝑥 2 +3𝑥−7
Six multiplications
𝑥( 𝑥 2 )+𝑥 3𝑥 −𝑥 7 −3( 𝑥 2 )−3 3𝑥 −3(−7)
𝑥 3 +3 𝑥 2 −7𝑥−3 𝑥 2 −9𝑥+21
Now combine like terms!
𝑥 3 −16𝑥+21
You can also use a multiplication table and add like boxes.

11. Using a table to multiply
𝑥 3 +6 𝑥 2 +𝑥−14

12. Multiply
#1 ( 𝑥 2 −5𝑥+2)(𝑥−6) #2 ( 𝑥 2 +3𝑥−10)(2 𝑥 2 −4𝑥+1) You can use a table or just multiply terms! Make sure you do all the required multiplications! TRY THESE!

13. How can you multiply more than two polynomials?
What do you do to multiply several numbers?
Find the product: (2𝑥−1)(𝑥+2)(3𝑥−4)

14. Special Cases Sum and Difference 𝑎+𝑏 𝑎−𝑏 = 𝑎 2 − 𝑏 2 𝑥−4 𝑥+4 =
𝑥−4 𝑥+4 =
Square of a binomial (𝑎+𝑏) 2 = 𝑎 2 +2𝑎𝑏+ 𝑏 2
(𝑥+3) 2 =
(𝑎−𝑏) 2 = 𝑎 2 −2𝑎𝑏+ 𝑏 2
(𝑚−5) 2 =

15. Cube of a binomial (𝑎+𝑏) 3 = 𝑎 3 + 3𝑎 2 𝑏+ 3𝑎𝑏 2 + 𝑏 3
(𝑝+3) 3 =
(𝑎−𝑏) 3 = 𝑎 3 − 3𝑎 2 𝑏+ 3𝑎𝑏 2 − 𝑏 3
(𝑧−6) 3 =

16. Try these!
Find the products! #1 4𝑐+5 4𝑐−5 #2 (3𝑚−1) 2 #3 (𝑟𝑠+2) 3

17. What if you had to find the following
(𝑥+2) 6
Any ideas?

18. Pascal’s Triangle can help to do a binomial raised to a power

19. Think about the binomials we raised and look for a relationship with Pascal’s Triangle

20. Use Pascal’s Triangle to expand the following.
(2𝑟−1) 5

21. Assignment #16
Pg. 170 #3,7,9,13,17-21 odd,25,29,34,35-41 odd, 45,47,51,56