1. Add, Subtract and Multiply Polynomials
Chapter 5.3
Add, Subtract and Multiply Polynomials

2. Combine Like Terms Using Addition!
Adding Polynomials
𝑥 3 −2 𝑥 2 +4𝑥+8
−3 𝑥 3 + 𝑥 2 −12𝑥−5
Adding Vertically
−2 𝑥 3 −𝑥 2 −8𝑥 +3
Adding Horizontally
𝑥 3 −2 𝑥 2 +4𝑥+8 + −3 𝑥 3 + 𝑥 2 −12𝑥−5 =
𝑥 3 + −3 𝑥 3 −2 𝑥 2 + 𝑥 2 +4𝑥+(−12𝑥)+8 + −5 =
Combine Like Terms Using Addition! +

3. Subtracting Polynomials
𝑥 3 −2 𝑥 2 +4𝑥+8
−3 𝑥 3 + 𝑥 2 −12𝑥−5
Subtracting Vertically
4 𝑥 3 −3𝑥 2 +16𝑥 +13
Subtracting Horizontally
𝑥 3 −2 𝑥 2 +4𝑥+8 − −3 𝑥 3 + 𝑥 2 −12𝑥−5 =
𝑥 𝑥 3 −2 𝑥 2 + − 𝑥 2 +4𝑥+(+12𝑥) =
Change the signs of the second polynomial & Combine Like Terms Using Addition! −

4. Subtract Horizontally
You Try
Add Vertically
Add Horizontally
2𝑥 3 −5 𝑥 2 +3𝑥−9
𝑥 3 + 6𝑥 2 +11
Subtract Vertically
Subtract Horizontally

5. Multiply one term with all the others.
Multiplying Polynomials
−2 𝑥 2 +3𝑥−6
𝑥−2
Multiplying Vertically
+4𝑥 2 −6𝑥 +12
−2𝑥 𝑥 2 −6𝑥
−2𝑥 3 +7𝑥 2 −12𝑥 +12
Multiply one term with all the others. ×
Multiply the next term with all the others. +
Combine Like Terms Using Addition!

6. Multiplying Polynomials
−2 𝑥 2 +3𝑥−6
𝑥−2
Multiplying Horizontally
(𝑥−2)×(−2 𝑥 2 +3𝑥−6)
−2 𝑥 3 +3 𝑥 2 −6𝑥 +4 𝑥 2 −3𝑥−6

7. Multiplying Binomials
(𝑥−2)(𝑥+3)(𝑥+1)
Multiplying Horizontally
𝑥 2 −2𝑥+3𝑥−6
𝑥 2 +𝑥−6
𝑥+1 𝑥 2 +𝑥−6
𝑥 3 + 𝑥 2 −6𝑥+ 𝑥 2 +𝑥−6
𝑥 3 + 2𝑥 2 −5𝑥+−6