Factoring ReviewGreatest Common Factor, Difference of Squares, Box Method, Quadratic Formula

Method 1: Greatest Common Factor Abbreviated GCF When to use it: When each term in the

equation share a common factor (may be a number, or a variable)

May also be a combo of the two

Steps in GCF

Find the common factor(s) in the equation Divide the entire equation by the GCF Pull it outside the equation by separating with

parentheses Set equal to zero Locates the x intercepts (roots) of the

equation

Y=-x2+6x

Y= 2x2+18x+28

Things to Watch out for with GCF You may be able to use another method to

finish factoring at times

Method 2: Difference of Squares When to use it: Two term equation If your terms are both perfect squares Separated by a – sign in the equation

Steps in Solving Using Difference of Squares Check that each term is a perfect square Check that they are separated by a minus

sign Take the square root of each equation Place each root in a set of parentheses, with

a subtraction sign in one set, and an addition sign in the other

Set each parentheses=0 and solve for x

Find the roots of Y=4x2-81

Find the x intercepts of y=x2-25

Solve for x: y=9x2+36

Things to watch out for with Difference of Squares

Method 3: Box Method

When to use it: When you have three terms to factor

Steps in Box Method

Find the zeros of y=X2+2x-3

Find the roots of y=x2-8x+12

Find the roots of y= 8x2-40x+50

Find the x intercepts of y= 2x2-5x+2

Find the roots of y=-16t2+63t+4

Things to watch out for with box method Need three terms Make sure they are in quad form Watch your negative signs Make sure you are only factoring the leading

coefficient and constant terms.

Quadratic Formula

You can always use the quadratic formula Sometimes there are just easier ways to

solve

The Quadratic Formula

a

acbb

2

42

What do the variables mean?

They represent the coefficients from the quadratic expression

Ax2+Bx+C=0 Keep in mind you only write out the

coefficients, not the x2 or x

Example

Use the quadratic formula to find the roots of x2 + 5x-14=0

Solve x2-7x+6=0

Solve 4x2=8-3x

Solve 2x2-6x=-3

Graphing Quadratics

Using the standard form Ax2+Bx+C=0 of a quadratic, you can create a graph by looking at several things

A tells you if the parabola opens up or down A>1, opens up, A<1, opens down C is the y intercept Factor and solve to find the x intercepts,

graph!

Factor, Solve and Graph

X2+6x=0 X2-3x-1=0 X2-5x-6=0 4X2=-8x-3 5x2-2x-3=0 -x2-3x+1=0