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When the polynomial f(x) is divided by x - 2, the remainder is 17. Determine the value f(2).

 

This might help

https://www.khanacademy.org/math/algebra2/arithmetic-with-polynomials/polynomial-remainder-theorem/v/polynomial-remainder-theorem-example

 

\(f(2)=17\)

f(x) / (x-2)    =   some polynomial ,let's call it P,  plus  a remainder of 17.

                    = ( P   + 17)

so f(x)          = (P   +17) (x-2)

so f(2)          = (P + 17) ( 2-2)       =  0

Melody is correct.

 

The Guest's answer is incorrect when he/she states that  f(x ) /(x - 2)  =  P + 17  (where 'P' is the quotient and 17 is the remainder); the correct expression should be:  f(x) / (x - 2)  =  P + 17 / (x - 2).

 

As an arithmetical example, let's say that you divide 30 by 13. This results in a quotient of 2 (which above is called 'P') and a remainder of 4, but, it is incorrect to say that 30/13  =  2 + 4; you need to say that 30/13 = 2 + 4/13.