Factoring Review Greatest Common Factor Difference of Squares

Factoring Review Greatest Common Factor, Difference of Squares, Box Method, Quadratic Formula

Method 1: Greatest Common Factor n n n 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 n n n 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=-x 2+6 x

Y= 2 x 2+18 x+28

Things to Watch out for with GCF n You may be able to use another method to finish factoring at times

Method 2: Difference of Squares n n n 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 n n n 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=4 x 2 -81

Find the x intercepts of y=x 2 -25

Solve for x: y=9 x 2+36

Things to watch out for with Difference of Squares

Method 3: Box Method n When to use it: When you have three terms to factor

Steps in Box Method

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

Find the roots of y=x 2 -8 x+12

Find the roots of y= 8 x 2 -40 x+50

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

Find the roots of y=-16 t 2+63 t+4

Things to watch out for with box method n n 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 n n You can always use the quadratic formula Sometimes there are just easier ways to solve

The Quadratic Formula

What do the variables mean? n n n They represent the coefficients from the quadratic expression Ax 2+Bx+C=0 Keep in mind you only write out the coefficients, not the x 2 or x

Example n Use the quadratic formula to find the roots of x 2 + 5 x-14=0

n Solve x 2 -7 x+6=0

n Solve 4 x 2=8 -3 x

n Solve 2 x 2 -6 x=-3

Graphing Quadratics n n n Using the standard form Ax 2+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 n n n X 2+6 x=0 X 2 -3 x-1=0 X 2 -5 x-6=0 4 X 2=-8 x-3 5 x 2 -2 x-3=0 -x 2 -3 x+1=0