Latest TCS Aptitude Question SOLUTION: In this question, A^B means A raised to the power B.Let f(x)=1+x+x^2+......+x^6.Then reminder when f(x^7) is divided by f(x)is: (a)6 (b)7 (c)0 (d)none

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(#M40153992) TCS Programming question reminder Keep an EYE

In this question, A^B means A raised to the power B.Let f(x)=1+x+x^2+......+x^6.Then reminder when f(x^7) is divided by f(x)is:
(a)6
(b)7
(c)0
(d)none

Asked In TCS joydip (8 years ago)

Unsolved Read Solution (5)

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Read Solution (5) :

somu  (8 years ago)

Given that f(x7)=1+x7+(x7)2 + ....+ (x7)6 = 1+x7+x14+....+x42
We will rewrite the above equation, f(x7)=1+(x7−1)+(x14−1)+... + (x42−1)+6
We know that x7−1=(x−1)(x6+x5+...1)
(∵ xn−an = (x−a).(xn−1+xn−2.a+xn−3.a2.....+an−1 )
Now It is clear that x7−1 is exactly divisible by f(x).
Also x14−1=(x7)2−12 and x7−1 is a factor of this expression. (∵xn−an is always divisible by x−a
Similarly, we write x21−1=(x7)3−13, x28−1=(x7)4−14....
So remainder = 1 + 6 = 7

Is this solution Helpfull? Yes (9) | No (5)  

sujeet kumar patel  (8 years ago)

put x=1,f(x)=7 and f(x^7)=7 sof(x)/f(x^7) gives reminder=0

Is this solution Helpfull? Yes (7) | No (9)  

anwasha halder  (8 years ago)

ans will be 7

Is this solution Helpfull? Yes (2) | No (1)  

Pooja shrivastava  (8 years ago)

0 if we put x = 1

Is this solution Helpfull? Yes (2) | No (1)  

Shubham Tariyal  (4 years ago)

D) none of the above

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