FACTORING POLYNOMIALS
1) First determine if a common monomial factor (Greatest Common Factor) exists. Factor trees may be used to find the
GCF of difficult numbers. Be aware of opposites: Ex. (a-b) and (b-a) These may become the same by factoring -1
from one of them.
2) If the problem to be factored is a binomial, see if it fits one of the following situations.
A. Difference of two squares:
B. Sum of two squares:
does not factor (it is prime).
C. Sum of two cubes:
Note: Resulting trinomial does not factor.
D. Difference of two cubes:
Note: Resulting trinomial does not factor.
E. If none of these occur, the binomial does not factor.
3) If the problem is a trinomial, check for one of the following possibilities.
A. Square of a binomial:
B. If , use reverse foil or trial and error method:
C. If , use trial and error method. (Grouping may also be used.)
4) If factoring a polynomial with four terms, possible choices are below.
A. Group first two terms together and last two terms together.
B. Group first three terms together.
C. Group last three terms together.
BE SURE YOUR ANSWERS WILL NOT FACTOR FURTHER!
All answers may be checked by multiplication.
PRACTICE PROBLEMS:
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ANSWERS:
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or
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MORE PRACTICE PROBLEMS:
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ANSWERS:
41.
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70. 71.
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MORE PRACTICE PROBLEMS:
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ANSWERS:
81.
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86. 87.
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ANSWERS:
121.
122.
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125.
126.
127.
128.
129.
130.
131.
132.
133. 134.
135.
136.
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138.
139.
140.
