Adding and Subtracting Polynomials

*** 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 5 + 12𝑥 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). ***

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

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

Solving Vertically

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

Homework: pg. 363, #s 12-18 pg. 366, #s 5-10, 12