Question

9) What is the result of the following calculation?

(x-a)*(x-b)*(x-c)*(x-d)*...* (x−y) + (x − 2) =
Note: There are 26 factors in this product...one for every letter of the alphabet.

Answer 1

x - 2

Explanation:

The given expression involves a product of factors and an additional term. However, due to a specific property of the factors, the entire product will become zero, making the calculation simpler than it initially appears. Let's break down the expression to understand why.

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The expression '(x - a) · (x - b) · (x - c) · (x - d) · ... · (x − y) + (x − 2)' consists of a product of 26 factors, each being the difference between x and a letter from the alphabet (from a to z), multiplied together. Additionally, there's a term '(x - 2)' being added.

Now, consider that each factor has the form:

⇒ (x − letter)

Where "letter" represents a letter from the alphabet.


When the letter is equal to x, the factor becomes:

⇒ (x − x),

Which is mathematically equivalent to 0.


Since there are 26 factors, each of which contains a term (x − letter), and one of them is (x − x) which equals 0, the entire product becomes 0.

Therefore, the result of the given calculation is 0 + (x - 2) = x - 2