Question

Use the remainder theorem to determine if x-2 is a factor if the polynomial f(x)=3x5-7x3-11x2+2

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Answer 1

Answer:

(x-2) is NOT a factor of the given polynomial.

Step-by-step explanation:

Is x-2 a factor of 3x5-7x3-11x2+2?  The quickest way to determine whether or not there's a remainder after division is to use synthetic division.  Use 2 as the divisor (this is derived from (x-2) ) and the six coefficients 3, 0, -7, -11, 0, 2 (derived from  3x5-7x3-11x2+2   ):

     ------------------------------------

2   /   3   0   -7   -11     0       2

              6  -12   -38 -98   -196

    -----------------------------------------        

       3     6    -19  -49 -98    -194      

Here we have a remainder (-194).  Whenever there's a non-zero remainder, we conclude that the possible factor being checked (x-2) is NOT a factor of the given polynomial, and 2 is NOT a root of that polynomial.