Question

check whether x2+3x+1 is a factor of 3 x4 + 5 x3 - 7x2 +2x +2.

Answer 1

As, remainder is zero
x² +3x+1 is a factor of polynomial 3 x4 + 5 x3 - 7x2 +2x +2.
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Answer 2

(3 x4 +5 x3 -7 x2 +2x+2)
=(x2 +3x +1)(quotient)  + (rem)
if rem=0 then it is a factor 
on dividing we get
quotient=(3 x2 -4x+2)
& rem=0
since rem=0   therefore it is a factor