# 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 |

## 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

Solving Word Problems Using Factored Form

Methods of Factoring + Examples