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Grade: 12
        
Cannot understand the explanation given for Example 93.What is the principle for questions of this nature?
one month ago

Answers : (3)

Arun
23742 Points
							
Dear student
 
Please attach clear image. I will be happy to help you.
 
Hope you understand.
 
Regards
Arun
one month ago
Vikas TU
10366 Points
							
Dear student 
Please specify that what is x-3 is it a polynomial given in some linked question ? 
We will help …..................
Good Luck 
one month ago
Aditya Gupta
1896 Points
							
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 :))
one month ago
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