Example Questions
例子问题# 21:Simplifying, Distributing, And Factoring
Simplify completely:
Example Question #22 :Simplifying, Distributing, And Factoring
Subtractfrom.
Example Question #23 :Simplifying, Distributing, And Factoring
Addto.
Example Question #24 :Simplifying, Distributing, And Factoring
Factor completely:
First, factor out the greatest common factor of the terms, which is:
The quadratic trinomial can be factored aswhereand; by trial and error we find that the numbers chosen are, so
Example Question #25 :Simplifying, Distributing, And Factoring
Simplify:
Apply the power of a quotient rule:
Example Question #26 :Simplifying, Distributing, And Factoring
Factor completely:
is a common factor of both terms, so factor it out:
cannot be factored, so this is the complete factorization.
Example Question #27 :Simplifying, Distributing, And Factoring
Factor completely:
First, we find two integers whose sum is 19 and whose product is. Through trial and error we find these integers are 3 and 16. We use these numbers to split the middle term, then we factor using the grouping method:
Example Question #28 :Simplifying, Distributing, And Factoring
Factor completely:
Factor by grouping as follows:
Example Question #29 :Simplifying, Distributing, And Factoring
Factor completely:
Factor by grouping as follows:
The first factor is the difference of squares, so further factoring can be done:
Example Question #30 :Simplifying, Distributing, And Factoring
Factor completely:
The polynomial fits the perfect square pattern:
This can be factored using the pattern
with: