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Chapter 10: Problem 3

If the product of two distinct integers is \(91,\) then which of the following values could represent the sum of the two integers? Indicate all possible values. a. -92 b. -91 c. 7 d. 13 e. 20

Short Answer

Expert verified
The possible sums of the two integers are -92 and 20.

Step by step solution

01

Factorize 91

To find the pairs of integers, we should factorize 91. Doing so, we find that 91 can be expressed as a product of 1 and 91 or -1 and -91, as well as 7 and 13 or -7 and -13.
02

Sum the pairs

Next, we add up the pairs of integers. Adding 1 and 91 gives us 92, -1 and -91 gives -92, 7 and 13 gives 20, and -7 and -13 gives -20.
03

Compare with the options

Comparing the calculated sums with the options provided, we find that a. -92, d. 13, and e. 20 are possible values for the sum of the two integers. However, option d is incorrect since it's not among our calculated sums.

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