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Cannot understand the explanation given for Example 93.What is the principle for questions of this nature?

Cannot understand the explanation given for Example 93.What is the principle for questions of this nature?

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Grade:12

3 Answers

Arun
25750 Points
4 years ago
Dear student
 
Please attach clear image. I will be happy to help you.
 
Hope you understand.
 
Regards
Arun
Vikas TU
14149 Points
4 years ago
Dear student 
Please specify that what is x-3 is it a polynomial given in some linked question ? 
We will help …..................
Good Luck 
Aditya Gupta
2081 Points
4 years ago
both answers above are trash. the correct explanation is ;
let g(x)= p(x) – 1.
now, g(3)= p(3) – 1= 1 – 1
or g(3)= 0. hence by factor theorem x – 3 is a factor of g(x) or in other words x – 3 divides g(x).
so, g(x)= (x – 3)*q(x) where q is another polynomial.
or p(x) – 1 = (x – 3)*q(x) or p(x)= 1 + (x – 3)*q(x). Since p has integer coeffs, q should also have integer coeffs.
now put x= 1 on both sides of this identity
p(1) – 1= (1 – 3)*q(1)
or 2 – 1= – 2q(1)
or q(1)= – ½ which is not possible since q had all integer coeffs and 1 is also an integer hence q(1) needs to be an integer as well.
kindly approve :))

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