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Answer:
The values of k will be:
Step-by-step explanation:
Let the expression of polynomial P be
Let the expression if the polynomial Q be
Plug in Q(x) = 0
0 = x+2
x = -2
As (x+2) is a factor of 3x²-4kx-4k²
substitute x = -2 in the the polynomial
3x²-4kx-4k² = 0
Write in the standard form ax²+bx+c = 0
Factor out common term -4
Factor k²-2k-3: (k+1)(k-3)
Using the zero factor principle
if ab=0, then a=0 or b=0 (or both a=0 and b=0)
solving k+1=0
k+1 = 0
k = -1
solving k-3=0
k-3=0
k = 3
Thus, the values of k will be:
