+116 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).
+129852 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
