Use synthetic division and the Remainder Theorem to find P(a): P(x)=x^4+x^3-5x^2+9x-6; a=3 (MULTIPLE CHOICE)

Question

Use synthetic division and the Remainder Theorem to find P(a): P(x)=x⁴+x³-5x²+9x-6; a=3

 

a. 78
b. 84
c. 3
d. 16

 

 

Answer 1

Start with Synthetic Division:

 

3|    1    1    -5    9    -6

             3    12   21    90

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

        1    4    7    30    84

 

The remainder theorem states that the remainder we just found, 84, is equal to P(3).