Math 10 Name: Unit 1: Factoring (Day 3)

Classifying Polynomials

Learning Intention(s):

Identify different types of polynomials Be able to identify and combine like terms Use distributive property to multiply binomials

Vocabulary: Terms: Monomial: Binomial: Trinomial: Polynomial: Coefficient: Constant: Degree: Like Terms:

Given the expression: 753 32 babba Identify the variables, coefficients, constants, degree of each term, degree of polynomial.

Adding Polynomials The easiest way to add polynomials is to:

1) Remove the brackets 2) Combine like terms

Examples:

1. (𝑥2 + 4𝑥 + 3) + (2𝑥2 + 5𝑥 + 1) 2. (3𝑦3 − 3𝑦 + 2𝑦2 + 8) + (−5 − 6𝑦2 + 2𝑦)

Subtracting Polynomials The easiest way to subtract polynomials is to:

1) Distribute a negative through brackets 2) Combine like terms

Examples:

1. (2𝑥 + 7) − (6𝑥 − 2)

2. (8 − 𝑛 − 𝑛2)— (−2 + 3𝑛 − 𝑛2)

Multiplying Monomials: 1. Multiply the coefficients 2. Combine the variables Examples: Multiply

1. (3𝑎)(4𝑏)

2. 5𝑎𝑏 ∙ 3𝑐

3. (−6𝑚2)(3𝑚𝑛)

4. (−2𝑏2𝑥𝑦4)(−3𝑏𝑥𝑦)

5. What is the area of the triangle below?

Area = base x height 2 3x 4x

Multiplying Polynomials by Monomials To multiply a monomial by a polynomial we must first remember how to distribute. Use the Distributive Property: acabcba )(

Examples: Expand

1. 2(2𝑎 − 5𝑑 + 4𝑐)

2. −3𝑥(𝑥2 − 2𝑥 + 5)

3. (−3𝑑)(−2𝑑 + 3)

4. 4𝑥(𝑥 − 3) − 2(𝑥 + 3)

5. 𝑎

4(6𝑎 − 4)

Evaluate the value of a polynomial when x=-4 1. −3𝑥2 + 2𝑥 − 1

a. 𝑥2 − 2𝑥 − 2

Find the area of the following shapes a) 95 x x3 b) x2 x3 x4 x2

Homework: 2.1 # 1, 2odd, 4odd, 5-9odd