SOLUTION: find the value of k so that (x^4 -2x^2 +kx+6) is divided by (x-2), the remainder is 0

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Question 1193950: find the value of k so that (x^4 -2x^2 +kx+6) is divided by (x-2), the remainder is 0
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
use 2synthetic division as shown below:



the last position in the synthetic division is 2k + 14.
if x - 2 is a factor of the equation, then 2k + 14 must be equal to 0.
solve for k to get k = -7.

here's a reference on synthetic division.
https://www.purplemath.com/modules/synthdiv.htm

replacing k in the original equation with -7, i get:
y = x^4 -2x^2 -7x + 6
the graph of that equation below shows that one of the zeroes of that equation is at x = 2.
the factor is (x - 2).




Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

find the value of k so that (x^4 -2x^2 +kx+6) is divided by (x-2), the remainder is 0
You don't have to go through all of what the other person stated in order to find the value of k, 
especially if you know nothing about or was never introduced to synthetic division.

As x - 2 is a factor, we get: x - 2 = 0, and x = 2, which means that 2 is one of the 4 zeroes
of this 4th power function, with the coordinate point, (2, 0).
Using the Remainder Theorem, and substituting (2, 0) for (x, y) in the equation gives us:

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