OA Explanation:Use Remainder Theorem for this onePlug-in \((x + 1) = 0\) i.e. \(x = -1\)
\(3(-1)^{2n+3} - 4(-1)^{2n+2} + 5(-1)^{2n+1} - 8\)
We can either have \(n\) as an odd or an even number
Case I: \(n\) is odd\(3(-1)^{odd} - 4(-1)^{even} + 5(-1)^{odd} - 8\)
\(3(-1) - 4(1) + 5(-1) - 8\)
\(-20\)
Case II: \(n\) is even\(3(-1)^{odd} - 4(-1)^{even} + 5(-1)^{odd} - 8\)
\(3(-1) - 4(1) + 5(-1) - 8\)
\(-20\)
Therefore the remainder will be \(-20\)
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I hope this helps!
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, Indiahttps://www.instagram.com/prepster_education/