Find Value of k

Section 2.3
Question 93

I seek the set up only. If no set up, then the steps for me to try on my own. Since (x - 4) is a factor of the polynomial involving k, I assume synthetic division can be used. Yes?

 

yes, use synthetic division

4| 1 -k 2k -8

 

Ok. I will give it a try.

 

See attachment. I got stuck after applying synthetic division.

 

you got a reminder R=56-8k

for x^3-kx^2+2kx -8 to be divisible by (x-4), reminder have to be equal to zero

so, 56-8k=0 ....solve for k

56=8k
k=56/8
k=7

then your equation x^3-kx^2+2kx -8 will be x^3-7x^2+14x -8

check:
x^3 - 7 x^2 + 14x - 8 = (x^2 - 3x + 2)*(x - 4) + 0 -> means x^3-kx^2+2kx -8 is divisible by (x-4) if k=7

 

What mistake did I make?

 

you did no mistake, I just finished what was needed to be done after your "stuck here"

 

Good to know I made no mistakes.