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Previously, we studied multiplication of polynomials (Section [link] ). We were given factors and asked to find their product , as shown below.
Given the factors 4and 8, find the product. . The product is 32.
Now, let’s reverse the situation. We will be given the product, and we will try to find the factors. This process, which is the reverse of multiplication, is called factoring .
The number 24 is the product, and one factor is 6. What is the other factor?
We’re looking for a number
such that
. We know from experience that
. As problems become progressively more complex, our experience may not give us the solution directly. We need a method for finding factors. To develop this method we can use the relatively simple problem
as a guide.
To find the number
, we would
divide 24 by 6.
The other factor is 4.
The product is
and one factor is
. What is the other factor?
We know that since
is a factor of
, there must be some quantity
such that
. Dividing
by
, we get
Thus, the other factor is .
Checking will convince us that is indeed the proper factor.
We should try to find the quotient mentally and avoid actually writing the division problem.
The product is
and
is a factor. Find the other factor.
Mentally dividing
by
, we get
Thus, the other factor is .
The product is 84 and one factor is 6. What is the other factor?
14
The product is and one factor is . What is the other factor?
In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor.
( [link] ) Simplify .
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