find the value of k, if x-3 is a factor of k^2x^3-x^2+3x+1
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find the value of k, if x-3 is a factor of k^2x^3-x^2+3x+1
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p(x) = k²x³-x²+3x+1
f(x) = x-3 = 0
=> x = 3
given that f(x) is a factor of p(x)
=> p(3) =0
=> k²(3)³ -(3)²+3×3+1= 0
=> 27k² -9+9+1 = 0
=> k² = -1/27
=> k = √(-1/27)