We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
234
1
avatar+86 

1. Suppose g(x) is a polynomial of degree five for which g(1) = 2, g(2) = 3, g(3) = 4, g(4) = 5, g(5) = 6, and g(6) = -113. Find g(0).

 

2. Suppose f(x) is a polynomial of degree 4 or greater such that f(1)=2, f(2)=3, and f(3)=5. Find the remainder when f(x) is divided by (x-1)(x-2)(x-3).

 Dec 15, 2018
 #1
avatar+103913 
+1

I know how to do the first one.....but.....not the second

 

1. Suppose g(x) is a polynomial of degree five for which g(1) = 2, g(2) = 3, g(3) = 4, g(4) = 5, g(5) = 6, and g(6) = -113. Find g(0).

 

The first one sets up a  system of 6 equations with 6 unknowns.....this is very tedious to solve by hand.....so....I'm not!!!....I'll let this website do the "heavy lifting" :

 

https://matrix.reshish.com/gauss-jordanElimination.php

 

 

Here is the system :  

 

a + b + c + d + e + f = 2

32a + 16b + 8c + 4d + 2e + f = 3

243a + 81b + 27c + 9d + 3e + f = 4

1024a + 256b + 64c + 16d + 4e + f = 5

3125a + 625b + 125c + 25d + 5e + f  = 6

7776a + 1296b + 216c + 36d + 6e + f = -113

 

We are only interested in the value of "f"   = 121

And this is   =   f(0)

 

BTW....the polynomial is

 

-x^5  + 15x^4 - 85x^3 + 225x^2 - 273x + 121

 

 

cool cool cool

 Dec 15, 2018

10 Online Users

avatar