Question

The sum of all possible values of n, where n is a non-zero integer when n2 + 8n + 6 is divided by n gives an integer, is

Please help.. I'll fail if you dont help

Answer 1

Step-by-step explanation:

The sum of all possible values of n, where n is an integer when 4n2 + 6n + 8 is divided by 2n gives an integer, is

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Answer 2

Concept

An integer is a number that can be written without a fractional component.

Given

1) n is a non-zero integer.

2) $n^2 + 8n + 6$ is divided by n gives an integer

FInd

1) sum of all possible values of n.

Solution:

4n²  + 6n   +  8 is divisible by n

$n\ |\ n^2 + 8n + 6 \ |\ (n + 8)$

     $n^2$

   __________

            $8n + 6$

            $8n$

           ________

                    $6$

6 must be divisible by n      

6 is divisible by 2, 3 or 6

Therefore,

$n = 2\ , 3, \ 6$

$Sum = 2 + 3+ 6 = 11$

Thus, sum of all possible values of n = 11