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Earlier discussion
2 older comments kept for context.
Oluwaseun Adeyemi
Since \(x-2\) is a factor, we can put \(x=2\) in the expression and equate it to zero to find k.
\(x^2-3x^2+kx+14 = 0\)
\(-2x^2+kx+14=0\)
\(-2(4)+2k+14=0\)
\(-8+2k+14=0\)
\(2k=8-14=-6\)
\(k=-3\)
Anthonette Ome Akpotu
the answer is -3