4.1/2 Quiz Flashcards
Four Types of Factoring
1) Greatest common factor
2) Trinomials where a=1
3) Trinomials where a>1
4) Difference of two squares
When Factoring, Always Look For
GCF first
Checking GCF
Re-distribute
Trinomials Where a=1
Three terms in standard form with no co-efficient
Factors in Standard Form
Add to b, multiply to ac
If Factors Add to Negative
Both values are negative
Trinomials Where a>1
Three terms in standard form where a is anything but one, includes co-efficient
Steps to Trinomials
1) Multiply a and c
2) Set the product to top value in diamond method
3) B is the sum, or bottom value in the diamond method
4) Find the factors and put them in factored form with a value
5) Reduce in each binomial
Box Method
Look across rows and columns for similarities
Difference of Squares
Binomial seperated by subtraction, variable then positive and negative GCF
Difference of Squares Formula
a^2-b^2=(a+b)(a-b)
Two Perfect Sqares Seperated by Addition
Prime and can no longer be factored
REMEMBER
Put equations in SF
Check for GCF
Leading term always takes the symbol
Sometimes the only factor is pulling out GCF
Check for difference of two squares
Difference of two squares must be one positive and one negative
Check if difference of two squares can continue
Check answer
Solution to a Quadratic Equation
Where the function intersects the x-axis
Other Names for Solutions in Quadratic Equations
Zeros, roots, x-intercepts
Write Solutions As
x=#,# from least to greatest
Two Solutions
Two x-intercepts
One Solution
One x-intercept, also called repeated roots
No Solutions
No x-intercepts
Different Ways to Solve Quadratic
1) Graphing, x-intercepts
2) Factoring, (x-p)(x-q)=0
3) Square Roots, x^2=c
4) Quadratic Formula, x=-b+/-√b^2-4ac/2a
5) Completing the Square, standard form to vertex form
6) Technology, calculator
Answering No Solutions
Write no real solutions
Steps to Solving Quadratics by Factoring
1) Move all terms to one side and set the equation equal to 0
2) Factor
3) Set each factor equal to 0 and solve for each x-value
4) Write your answer as list of zeros
List of Zeros
x=#,# from least to greatest
