Solve the following and show solution.☺️

Question

Let P(x) = 3x³-4x²+8x-5. Evaluate P(x) by substituting in the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division. 

(a) P(2)                   (b) P(-1)

 

Answer 1

I will do the first one for you.

 

 

P(2) = 3(2)³ - 4(2)² + 8(2) - 5

       = 24 - 16 + 16 - 5

       = 19

 

 

Using synthetic division,

 

2 | 3       -4         8       -5

 

               6         4        24

_________________________

     3        2        12       19

 

 

By remainder theorem, we have

 

P(2) = (2 - 2)(3(2)² + 2(2) + 12) + 19