Quadratic Relationships
Factored Form
Learning Goals
- Learn how to factor an equation
- Learn the different methods of factoring
- Learn to tell the difference between a Common Binomial, Simple Trinomial, Complex Trinomial, Perfect Square, Difference of a Square
- How to find the G.C.F from an equation
- Steps to doing different types of factoring
Summary of the Unit y = a(x-r) (x-s)
- The value of a gives you the shape and direction of opening
- The value of r and s give you the x-intercepts
- To find the y-intercept, set x=0 and solve for y
- Solve using the factors
- Types of Factoring:
- Greatest Common Factor
- Simple factoring (a=1)
- Complex factoring (a does not equal 1)
- Special case - Difference of squares (Binomial)
- Special case – Perfect square (Trinomial)
Common Factoring
Equation: 4x+6
Factor: 2(2x+3)
G.C.F: 2
Simple Factoring
Equation x^2+5x+6
Factor: (x+2)(x+3)
Sum=5
Product=6
Complex Factoring
Equation: 6x^2+29x+35
Factor: (2x+5)(3x+7)
Sum: 29
Product: 6x35= 210
Difference of a Square
Equation: x^2-25
Factor: (x+5)(x-5)
-Square both numbers
Perfect Square (Positive)
Equation: a^2+2ab+b^2
Factor: (a+b)^2
Square the first and last term then multiply by 2 for the middle number. Positive signs = Positive factor
Perfect Square (Negative)
Equation: a^2-2ab+b^2
Factor: (a-b)^2
Square the first and last term then multiply by 2 for the middle number. Negative sign = Negative factor
Solving Word Problems Using Factored Form
Methods of Factoring + Examples