A number r when divided by 8 leaves remainder 3. What will be the remainder when (r² + 6r + 7) is divided by 8?

Question

Accepted Answer

Given that when r is divided by 8, the remainder is 3. This means r ≡ 3 (mod 8).

We need to find the remainder when (r² + 6r + 7) is divided by 8.

Step 1: Substitute r ≡ 3 (mod 8) into the expression:

r² + 6r + 7 ≡ 3² + 6×3 + 7 (mod 8)
= 9 + 18 + 7 (mod 8)
= 34 (mod 8)

Step 2: Find 34 mod 8:

34 ÷ 8 = 4 remainder 2 (since 8×4=32, 34-32=2)

So, the remainder is 2.

However, the options given are 4, 3, 1, 2. The calculation shows remainder 2.

Double-checking calculation:
9 + 18 + 7 = 34
34 mod 8 = 2

So the remainder should be 2.

Therefore, the correct answer is option 4: 2.

Answer

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