is (X+1)is a factor of the polynomial x⁹⁹⁷+x⁸⁸⁶+x⁷⁷⁵+x⁶⁵⁴+x¹¹³+1?
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Answer: yes
Step-by-step explanation:
to solve this question,use remainder therom ,
if x+1 is a factor then x=-1 should have value 0 in the polynomial
now -1 ^( even number ) = +1
and -1^(odd number ) =-1
and 997, 775,113 are odd
so you will have a equation
x⁹⁹⁷+x⁸⁸⁶+x⁷⁷⁵+x⁶⁵⁴+x¹¹³+1= -1+1-1+1-1+1
which is equal to 0 , so yes x+1 is a factor of x⁹⁹⁷+x⁸⁸⁶+x⁷⁷⁵+x⁶⁵⁴+x¹¹³+1
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