Factoring Review Notes
So far, we have learned how to factor polynomials several different ways. The ways that we have
learned include
1)
2)
3)
4)
5)
6)
The GCF method
Factoring by grouping
Factoring the difference of 2 squares
Factoring the sum of 2 cubes
Factoring the difference of 2 cubes
Factoring using the box method.
Knowing which of these methods to use when is difficult to determine sometimes.
Next to the description below, tell which method of factoring I should use from the list above. You may
put the number of the correct method above in the black next to the appropriate description.
A) You would use this method if your problem had three terms. The terms could not have a
greatest common factor. The coefficients of each term are an integer, where the first coefficient
is positive. Furthermore, the exponents on the variables of the terms have a pattern to them,
where the first is an even number exponent, the exponent on the variable of the second term is
half of the exponent of the first term, and the last term does not have a variable. This order of
the exponents could also be reversed. __________________
B) This method is used if your problem has two terms with a minus sign between them. The first
term and the last term could have variables with exponents, but the exponents would have to
be divisible by 3. Also, the coefficients of the first and last term would have to have cube roots.
_______________________________
C) When using this method, you must have at least two terms and the terms would have to have a
greatest common factor. You could have any number of variables and any number of
exponents. _____________________________
D) When using this method, you must have 4 terms. All of the terms do not have a greatest
common factor, but pairs of the terms do. Usually the first two terms of the problem, and the
last two terms, have a greatest common factor. The variables or their exponents do not form a
particular pattern.____________________________
E) This method is used if your problem has two terms with a plus sign between them. The first
term and the last term could have variables with exponents, but the exponents would have to
be divisible by 3. Also, the coefficients of the first and last term would have to have cube roots.
______________________________
F) This method is used if your problem has two terms with a minus sign between them. The first
term and the last term could have variables with exponents, but the exponents would have to
be divisible by 3. Also, the coefficients of the first and last term would have to have cube roots.
_____________________________________
Next, please list below the formulas for factoring the 3 special cases
1) The difference of two squares ______________________________________________
2) The difference of two cubes______________________________________________
3) The sum of two cubes __________________________________________________
Today as a review for our test I have given a worksheet entitled “factoring mixed review”. On the space
below, please write the method listed on the first page that you would use in order to factor the
problems on the “Factoring mixed review worksheet”
Problem Number
1) _______________________
11) _______________________
2) _______________________
12) _______________________
3) _______________________
13) _______________________
4) _______________________
14) _______________________
5) _______________________
15) _______________________
6) _______________________
16) _______________________
7) _______________________
17) _______________________
8) _______________________
18) _______________________
9) _______________________
19) _______________________
10) _______________________