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Solving a Quadratic Equation by Factorization Method

The differenc...

Question

The difference between the squares of two consecutive odd integers is always divisible by

A

8

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B

7

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C

6

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D

3

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Solution

The correct option is A 8
Let the two consecutive odd integers be $(2 x + 1)$ and $(2 x + 3)$
$∴ (2 x + 3)^{2} - (2 x + 1)^{2} = 4 x^{2} + 12 x + 9 - 4 x^{2} - 4 x - 1$
$= 8 x + 8 = 8 (x + 1)$
Hence, the difference is divisible by $8$

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