Question

use the synthetic division and the Remainder Theorem to find P(a). P(x)=x^4+x^3-5x^2+9x-6; a=3a.) 78b.)84c.)3d.)16

Answer 1

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

`p(3)\text{ = \lparen3\rparen}^4+(3)\placeholder{⬚}^3-5(3)\placeholder{⬚}^2+9(3)-6=81+27-45+27-6=84`

The answer is:

p(a) = p(3) = 84