SOLUTION: The cubic polynomial f(x) is such that the coefficient of x^3 is -1 and the roots of the equation f(x) = 0 are 1, 2 and k. Given that f(x) has a remainder of 8 when divided by x –

Algebra ->  Test -> SOLUTION: The cubic polynomial f(x) is such that the coefficient of x^3 is -1 and the roots of the equation f(x) = 0 are 1, 2 and k. Given that f(x) has a remainder of 8 when divided by x –       Log On


   

Question 695861: The cubic polynomial f(x) is such that the coefficient of x^3 is -1 and the roots of the equation f(x) = 0 are 1, 2 and k. Given that f(x) has a remainder of 8 when divided by x – 3, find
(a) the value of k,
(b) the remainder when f(x) is divided by x+3.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The factoring of such a cubic polynomial would be
f%28x%29=%28-1%29%28x-1%29%28x-2%29%28x-k%29
so that each factor would be zero for each of the roots of f%28x%29=0.

The remainder of f%28x%29 when divided by %28x-3%29 is
f%283%29=%28-1%29%283-1%29%283-2%29%283-k%29=8 --> %28-1%29%282%29%281%29%283-k%29=8 --> 2k-6=8 --> 2k=8%2B6 --> 2k=14 --> highlight%28k=7%29
and f%28x%29=%28-1%29%28x-1%29%28x-2%29%28x-7%29

The remainder of f%28x%29 when divided by %28x%2B3%29 is