SOLUTION: Is there anyone that can help me with this problem? I have worked almost the entire thing but am comfused toward the end. 1. Find all values of K such that f(x)is divisible bt t

Question 110328This question is from textbook Fundamentals of Alg and Trig
: Is there anyone that can help me with this problem? I have worked almost the entire thing but am comfused toward the end.
1. Find all values of K such that f(x)is divisible bt the given linear poly.
f(x) k^2x^3-4kx+3; x-1
This is what I did:
f(1)= k^2(1)^3-4k(1)+3
f(1)= k^2-4k+3
(k+1)(k-4)
THis factoring isn't working. I have made a mistake somewhere but I can;t tell where. Please help.
Thanks
This question is from textbook Fundamentals of Alg and Trig

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find all values of K such that f(x)is divisible bt the given linear poly.
f(x)= k^2x^3-4kx+3; x-1
-----------------------------
The Remainder Theorem says guarantees that (x-a) is a factor of
f(x) if f(a)=0.
-----------------
You are dividing by (x-1).
Find f(1) = k^2(1^3)-4k(1)+3
f(1)= k^2-4k+3
------------
Solve k^2-4k+3=0
(k-3)(k-1)=0
k=3 or k=1.
---------------
Those are the values of k which will guarantee f(x) being divisible
by (x-1)
===============
Cheers,
Stan H.

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