A number r when divided by 8 leaves remainder 3. What will be the remainder when $ (r ^ 2 + 6r + 7) $ is divided by 8?
A number r when divided by 8 leaves remainder 3. What will be the remainder when $ (r ^ 2 + 6r + 7) $ is divided by 8?
यदि किसी संख्या r को 8 से विभाजित करने पर शेषफल 3 प्राप्त होता है,तो $(r^2 + 6r + 7)$ को 8 से विभाजित करने पर शेषफल क्या होगा?
Detailed Solution & Logic
2
Given,
When r is divided by $8$, the remainder is $3$.
So,
$r = 8k + 3$
Now,
$r^2 + 6r + 7$
$= (8k + 3)^2 + 6(8k + 3) + 7$
$= 64k^2 + 48k + 9 + 48k + 18 + 7$
$= 64k^2 + 96k + 34$
$= 8(8k^2 + 12k + 4) + 2$
Hence, the remainder when divided by 8 is 2.
Answer: 2
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