factoring Algebra II Dr. Guram

Focus Questions How do we factor quadratic expressions of the form 𝑥 2 +𝑏𝑥+𝑐. How do we factor quadratic expressions of the form 𝑎𝑥 2 +𝑏𝑥+𝑐. What is an example of a real-world scenario where factoring is useful?

Curriculum standards CLE 3103.3.12, 3103.3.7, 3103.3.2, 3103.3.13 - understand the relationship between real zeros of a function and the x-intercepts of its graph. Sources: http://www.corestandards.org/Math/Content/HSA/CED /A/1/ Spring Board Algebra 2 workbook Larson algebra 2 textbook

Real World Examples Utilizing factoring What are examples of ways we utilize factoring in real world situations? ???

Real World Examples Utilizing factoring Finance Numerical analysis

Academic language Monomial: an expression that is either a number, a variable, or the product of a number and one or more variables with whole number exponents. binomial: the sum of two monomials. trinomial: the sum of three monomials.

Academic language Quadratic equation with one variable: an equation that can be written as 𝑎𝑥 2 +𝑏𝑥+𝑐 = 0 where 𝑎≠0. Root of an equation: the solutions of a quadratic equation are its roots. Zero of a function: a number k is a zero of a function f if f(K)=0.

Factoring example

Factoring solution House method on board

Factoring guided practice examples

Special Factoring patterns

Special Factoring patterns

Factoring guided practice examples

Zero product property

Zero product property example

Zero product property solution

Real World Example

Real World Solution

Zeros of a function

Zeros of a function

Factor with special patterns

Factor with special patterns example

Factor with special patterns example

Real world example

Real world solution

Review How do we factor quadratic expressions of the form 𝑥 2 +𝑏𝑥+𝑐. What is an example of a real-world scenario where factoring is useful?

Review of terms define the mathematical terms: monomial, binomial, and trinomial. Define the mathematical terms: quadratic equation, root of an equation, and zero of a function.

Classwork/Homework - Factoring worksheet