2 kinds of thinking problems

[Guest]

Hey,
Im having trouble with these two problems.
1. If (x-1) is a factor of x^3-2kx^2+3x+1, what is the value of k?



2. Prove that (x-a) is a factor of x^3-(a+b+c)x^2 + ( ab+bc+ca)x-abc?

Could any one help me figure these two out? thnks for your time.

 

[askmemath]

If X-1 is a factor that implies that X = 1 will satisfy the given equation
So in place of X we simply put 1

x^3-2kx^2+3x+1= 0
1^3 -2k(1^2)+3(1)+1 = 0
1-2k+3+1 = 0
5-2k = 0
Adding 2k on both sides
5 = 2k
Dividing by 2 on both sides
k = 5/2

Now by the same principle as above if X-a is a factor then X = a should satisfy the given equation.

Can you solve this part?

Come back with a repost if you get stuck somewhere.