Perform the divisions, using synthetic division .

p. 234.  #3.   

Solution:     First write down the coefficients of the polynomial, which are  and prepare to do synthetic division with .

Of  the resulting numbers   , the last number  is the remainder.  The first three numbers  are the coefficients of the quotient.  The quotient always begins with an exponent that is one less than the highest power of the polynomial.  The quotient will therefore begin with .  The quotient is  , and the final answer is  

5.    

Solution:  First you must re-write the numerator in the correct order—that is write it in descending powers of the variable, and include placeholder zeros for any terms that are missing.  Notice that the highest power of  is , and there is no  term. 

As always with synthetic division.  first write down the coefficients of the polynomial, which are  and prepare to do synthetic division with .

Of  the resulting numbers   ,  of course the last number  is the remainder, and the first four numbers  are the coefficients of the quotient.  Since the quotient always begins with an exponent that is one less than the highest power of the polynomial, the answer begins with .  

The final answer is .

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