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Answer:
k = - 2
Step-by-step explanation:
If (x - 1) is a factor of f(x) then f(1) = 0
f(x) = [tex]x^{10}[/tex] - k[tex]x^{7}[/tex] - 3 , then
f(1) = [tex](1)^{10}[/tex] - k[tex](1)^{7}[/tex] - 3 = 0 , that is
1 - k - 3 = 0
- 2 - k = 0 ( add 2 to both sides )
- k = 2 ( multiply both sides by 1 )
k = - 2