(N) is a whole number which when divided by 4 gives 2 as remainder. What will be the remainder when 2𝑁2+32𝑁2+3 is divided by 4?2130
Question
(N) is a whole number which when divided by 4 gives 2 as remainder. What will be the remainder when 2𝑁2+32𝑁2+3 is divided by 4?2130
Solution
The given condition is that N is a whole number which when divided by 4 gives 2 as remainder. This means that N can be written in the form of 4k+2, where k is any integer.
The expression given is 2N^2 + 3. Substituting N = 4k+2 in this expression, we get:
2(4k+2)^2 + 3 = 2(16k^2 + 16k + 4) + 3 = 32k^2 + 32k + 8 + 3 = 32k^2 + 32k + 11.
Now, we need to find the remainder when this expression is divided by 4.
The terms 32k^2 and 32k are divisible by 4, so they will not contribute to the remainder.
The remainder will be the remainder of 11 divided by 4, which is 3.
So, the remainder when 2N^2 + 3 is divided by 4 is 3.
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