1. Adding and Subtracting Polynomials

2. *** ALWAYS written in descending order (called standard form). ***
What is a polynomial?
Number of Terms
Name
One Term
Monomial
Two Terms
Binomial
Three Terms
Trinomial
Four or More Terms
Polynomial
4𝑥 𝑥 3 + 𝑥 2 −𝑥+5
Leading Coefficient – coefficient of the first term of the polynomial = 4
Degree of Polynomial – exponent of first term of the polynomial = 5
Degree of a Term – exponent of any term - 12𝑥 3 = 3
*** ALWAYS written in descending order (called standard form). ***

3. Adding Polynomials
(𝟑𝒙 𝟐 −𝟑𝒙−𝟓)+(𝟐 𝒙 𝟐 +𝟓𝒙+𝟑) Distribute the Positive: 𝟑𝒙 𝟐 −𝟑𝒙−𝟓+𝟐 𝒙 𝟐 +𝟓𝒙+𝟑 Identify Like Terms: 𝟑𝒙 𝟐 −𝟑𝒙−𝟓+ 𝟐𝒙 𝟐 +𝟓𝒙+𝟑 Combine Like Terms: 𝟓𝒙 𝟐 +𝟐𝒙−𝟐

4. Subtracting Polynomials
(𝟐𝒙 𝟑 + 𝟖𝒙 𝟐 +𝒙+𝟏𝟎)−(𝟓 𝒙 𝟐 −𝟒𝒙+𝟔) Distribute the Negative: 𝟐𝒙 𝟑 + 𝟖𝒙 𝟐 +𝒙+𝟏𝟎−𝟓 𝒙 𝟐 +𝟒𝒙−𝟔 Identify Like Terms: 𝟐𝒙 𝟑 + 𝟖𝒙 𝟐 +𝒙+𝟏𝟎−𝟓 𝒙 𝟐 +𝟒𝒙−𝟔 Combine Like Terms: 𝟐𝒙 𝟑 + 𝟑𝒙 𝟐 +𝟓𝒙+𝟒

5. Solving Vertically

6. Practice
Number 1:
(𝟐𝒙 𝟐 +𝟑𝒙+𝟗)+(− 𝒙 𝟐 −𝟒𝒙−𝟔)
Number 2:
(𝟐𝒙 𝟐 +𝟑𝒙+𝟐)−(− 𝟓𝒙 𝟐 −𝟐𝒙−𝟗)

7. Homework: pg. 363, #s pg. 366, #s 5-10, 12