when ax^2+bx+c is divided by x-1, the remainder is 10 if the same poly. is divided by x+2 the remainder is 1. x+1 is a factor of the polynomial. Find a,b, and c.

Answer 1

let f(x) = ax^2 + bx + c
given f(1) = 10
10 = a + b + c (#1)

given f(-2) = 1
1 = 4a - 2b + c (#2)

given f(-1) = 0 , .... (it said x+1 is a factor)
0 = a - b + c (#3)

#1 - #3
10 = 0 + 2b + 0
b = 5

#2 - #3
1 = 3a - b + 0 , but b=5
6 = 3a
a = 2

in #1
2 + 5 + c = 10
c = 3

a=2, b=5, c=3