Suppose we have the polynomial function p(x) = x^5-21x^4-23x^3+16x^2-6x+18. find the value of p(5) using synthetic division.

Answer 1

Hello,

Based on the remainder theorem, if you divide your polynomial by (x-5), the remainder of the division will be equal to P(5). So by using the synthetic division :

5 | 1 -21 -23 16 -6 18

| 5 -80 -515 -2495 -12505

|____________________________________________________________

1 -16 -103 -499 -2501 -12487

Since the last number in the answer line is the remainder, therefore P(5) = -12487