In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
P(x) = x^4 + x^3 - 5x^2 + 9x - 6
a = 3
Step 02:
Synthetic division:
3 | 1 1 -5 9 -6
|
_____3 __12__21__90_______
1 4 7 30 84
remainder = 84
Remainder Theorem:
p(a):
a = 3
[tex]p(3)\text{ = \lparen3\rparen}^4+(3)\placeholder{⬚}^3-5(3)\placeholder{⬚}^2+9(3)-6=81+27-45+27-6=84[/tex]The answer is:
p(a) = p(3) = 84
