# Factored Form

### Quadratic Relations

## Learning Goals for Unit

- Factor Binomials and Trinomials
- Use factored form to find AOS

## Factored Form: a(x-r)(x-s)

- The value of
**a**gives you the shape and direction of opening - The value of
**r**and**s**are the 2 x-intercepts (s,0) and (r,0) - To find the y-intercept (0,y) set x=0 then solve for y
- To find the axis of symmetry, add both x-intercepts and divide by 2
- To find the vertex, use the zeros (x-intercepts) to find the AOS and sub this x value into the equation to solve for y.

## Graphing Factored Form

## Types of Factoring

## Monomial Common Factor:

This means you must find a number that is a multiple of all numbers in the equation, also find a variable present in all numbers and put it outside the brackets.

## Binomial Common Factors:

## Factoring by Grouping:

Then perform the same steps used for monomial factoring.

## Factoring Trinomials (from Standard form) a^2+bx+c

So this means you must find 2 number who's sum is B and the product is C.

You then take factors of b, input them into the equation, removing b but keeping the variables.

Then factor by grouping, for both groups the numbers inside the brackets should be the same. You then take the numbers outside the brackets and put them together.

## Factoring Complex Trinomials

To solve this, you multiply c by the coefficient of a, use this new number and perform the steps used in regular trinomial factoring while keeping c the same in the equation.

## Special Product: Difference of squares

a2 - b2

Useful because it can be factored from(a+b)(a−b) to a^2-b^2

## Special Product: Perfect square trinomials

## Application Problems

2(x² +2x -168) = 0

(Factor)

(x+14)(x-12)

14² + 12² = 340

196+ 144+340

Therefore the integers are 12 and 14