Question
Download Solution PDFA number n when divided by 6, leaves a remainder 3. What will be the remainder when (n2 + 5n + 8) is divided by 6?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept used:
Euclid's Division Lemma, Dividend= Divisor (Quotient)+ Remainder
Calculation:
Number= n
So, by Euclid's Division Lemma
n= 6q+ 3
Also, (n2 + 5n + 8) when divided by 6 leaves a remainder, say r.
Therefore, (n2 + 5n + 8)
(6q+3)2 + 5(6q+3) +8
36q2+ 9+ 36q+ 30q+ 15+ 8
36q2+ 66q+ 32
Now, consider each of the terms above separately to see what the remainder is when they are divided by 6.
36q2 is divisible by 6 as 6 is divisible by 6. Hence, remainder is 0.
66q is divisible by 6 as 66 is division by 6. Hence, remainder is 0.
32 when divided by 6 leaves a remainder 2.
Hence, remainder for (n2 + 5n + 8) is 2.
Last updated on Jun 13, 2025
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