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Terms in this set (61)
What is the equation for solving difference of Squares?
ax^2 - c
All GCfs are whole numbers
True
All questions relating to GCF and Dos have two answers
False
You must factor with GCF
True
A way to factor with GCF
Find zeros and sketch the graph
do you factor or find the greatest common factor first?
Find greatest common factor
What do you put when doing difference of squares for ax^2-C^2
(ax-c)(ax+c)
What do you do when factoring with GCF if you cant find 2 numbers that multiply to C and add to make B
You multiply C by A and take it out later
What do you do for 6X^2-216
You should divide both sides by 6 and move six out and solve it like a normal difference of squares.
(ax-c)(ax+c) C^2=(216/6)^2
What is the equation for solving difference of Squares?
ax^2 - c
How do you factor 6x^2 - 216?
1. Divide each number by 6
~ 6x^2 - 216
/6 /6
~6(x^2 - 36)
2. Factor out terms
~6(x - 6)(x + 6)
How do you factor 5n^2 - 50n + 80 using GCF?
1. Find a factor that can be divided into all the terms.
~5n^2 - 50n + 80
/5 /5 /5
~5(n^2 - 10n + 16)
2. Factor out each term
~ 5(n - 8)(n + 2)
What does DoS stand for?
Difference of Squares (i.e. x squared or x cubed)
What is a perfect square?
It can divided by a whole number. For example: 4, 9, 16, 25, 36...
What is the most that a parabola can curve through on a graph?
3 roots
you can use a what short cut in subtraction problems
a square short cut
the biggest number that can go into several numbers is the
Greatest Common Factor
when do you leave the GCF on the outside of the ( )
when factoring with the GCF
What does it mean to be a perfect square?
A perfect square is a number that has a whole number square root. For example, 25 is a perfect square because 5 is a whole number.
How many possible answers are there when factoring with a GCF (Greatest Common Factor)?
There may be up to 3 answers.
What type of graph do you get when graphing GCF?
A parabola. The line may curve through 3 roots.
What does DoS stand for?
Difference of Squares
What is the equation for DoS?
ax^2-C
What is the GCF?
Greatest Common Factor
What expression do you use to solve the difference of squares?
ax²-c
What does the answer look like using variables?
(x-a)(x+a)
True or False: If the "a" value is negative then graph will open down.
true
True or False: If the "a" value is positive then the graph will open down.
false
With differences of squares you have to ?
Make a perfect square with your solution
The difference of squares can only be used when ______?
when "c" is negative.
All parts of the equation must be solved using the zero product property, including the numbers outside the parentheses. True or False?
True
When using the difference of squares, there must be a positive and a negative when factoring. True or False?
True
factor; x^2 - 49
(x-7)(x+7)
True or False: If the "a" value is negative then graph will open down.
true
Factor; 4v^2-9
(2v-3)(2v+3)
What is the difference of squares equation?
ax^2-c
What is GCF?
The closest number in which two (or more) numbers can fit into.
x^2+49 -- Why can the Difference of Squares method NOT be applied to this equation?
The "+" sign must be "-" or else the "b" value will not be zero.
When factoring with the GCF, is it possible to have three possible answers?
Yes
What is the first step when solving this problem?
16x³+8x-18x=-2x+8x³
Get all of the terms on one side of the =
What square roots would you use when solving this problem?
36x²-121
6 and 11
Greatest Common Factor (GCF)
The greatest factor that divides two numbers.
Difference of Squares (DoS)
The difference of two squares that can be factored.
First Step of Factoring
Find the GCF of all three numbers.
GCF (Greatest Common Factor)
# in which two or more #s are evenly divisible by
axSQUARED-c
Difference of squares
the difference of square shortcut only works if
it is a subtraction problem
when factoring with GCF you have to pick
the biggest number that can go into all three numbers in the problem
when factoring with GCF you have to remember
to leave the GCF on the outside of the ( )
What can be used to solve this equation 9r^2+36?
Difference of squares
What do you have to make the answer when you are done solving a problem with an x^2?
You have to make the answer plus or minus
What can you do to the square root of 9/10?
You can separate the top and the bottom to make it easier to solve
What is the basic formula when using difference of Squares?
(X-A)(X+A)
What is one of the most important steps when factoring with GCF?
Making sure you pull out not only the number but also the GCF of variable
What is the greatest number of answers you can get for your variable?
3, 1 for each factor and one for the items pulled out for GCF
What are the different ways you can factor a quadratic
By using the greatest common factor or the differences of squares
What does your quadratic need to have in order to use the differences of squares
a and c must be perfect squares
If you have a quadratic with values on both sides of the = what must you do
Combine like terms
When simplified, what will the problem 2x(16x²-25) become?
2x(4x-5) (4x+5)
What happens when the equation has a perfect square?
The simplified equation will have the variable - the square root and the variable + the square root.
When given the equation 12x³-18x²-24x, what can be used to factor it?
The Greatest Common Factor.
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