Question

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

Answer 1

Answer:

For given polynomial $P(a)=a^3+2a^2-3a+5=41$ and when a=3 is

$P(3)=41$

Step-by-step explanation:

Given polynomial is $P(x)=x^3+2x^2-3x+5$

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 $P(x)=x^3+2x^2-3x+5$ 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

$P(a)=a^3+2a^2-3a+5$

To find P(a):

$P(a)=a^3+2a^2-3a+5$

put a=3

$P(3)=3^3+2(3)^2-3(3)+5$

$P(3)=27+18-9+5$

$P(3)=41$

Therefore for given polynomial $P(a)=a^3+2a^2-3a+5=41$ when a=3 is  $P(3)=41$