Use synthetic division and the remainder theorem to find p ( a).
p(x)= x^3+2 x^2-3x+5, a=3

For given polynomial and when a=3 is

Step-by-step explanation:

Given polynomial is

Remainder Theorem:

To evaluate the function f(x) for a given number "a" you can divide that function by x - a and your remainder will be equal to f(a). Note that the remainder theorem only works when a function is divided by a linear polynomial, which is of the form x + number or x - number.

By using synthetic division for given polynomial and factor is (x-a)    (here x-3 is a factor given)

_3|    1      2       -3         5

        0     3       15       36

      ___________________

         1      5       12      | 41

Given polynomial can be written as

To find P(a):

put a=3

Therefore for given polynomial when a=3 is  

4.5(4 − x ) + 36 = 202 − 2.5(3x + 28) now multiply from the paranthesis

18 -4.5x + 36 = 202 -7.5x + 70 will add the numbers

54-4.5x = 272-7.5x move x to the left and numbers to the right

7.5x-4.5x = 272-54 make the difference

3x = 218 and divide by 3

x= 72