Problem Study (Polynomial Division)

1.   If is a factor of , Find the values of and
Solution 
Let  .
Since is a factor of , the remainder when is divided by is 0.
By polynomial long division we can find the remainder.  




 
Hence we have
 
and .
Similarly, we can say , 
When , and
When , .
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 2.   If is divisible by , prove that .
Solution 
 Since is divisible by , The remainder when is divided by = is zero.
By polynomial long division,











and .
.