If the sum (461 + 462 + 463 + 464) is evenly divisible by ?, determine ? =_____________?
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Answer: D. None of these
Explanation
The sum involves sequential powers of forty six which can be factored using polynomial expansion techniques. Factoring out common terms from the expression reveals its underlying algebraic divisibility properties. Evaluating the resulting factors shows divisibility by numbers not present among the first three options. Polynomial factoring allows complex sums of powers to be expressed as products of simpler integer factors. Divisibility rules determine whether an integer can be divided evenly by a divisor without leaving a remainder. Algebraic identities simplify calculations involving repeated exponentiation and summation operations.
Number theory applications use exponential factoring to study divisibility patterns in large integer sequences. Cryptographic algorithms rely on properties of prime factors and modular arithmetic to ensure data security. Mathematical problem solvers apply algebraic expansion rules to simplify complex number expression queries. Option A is incorrect because the expression is not evenly divisible by the number three. Option B fails to divide the factored polynomial sum without leaving a remainder. Option C does not match the prime factors derived from the algebraic expansion of the expression.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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