2. Given f(x)=kx+6 and x+ 2 is a factor of f(x) then what is the value of k?

Step 1 ：The problem is asking for the value of k in the function \(f(x) = kx + 6\), given that \(x + 2\) is a factor of \(f(x)\).

Step 2 ：A factor of a polynomial is a value that, when substituted into the polynomial, results in a value of zero. Therefore, if \(x + 2\) is a factor of \(f(x)\), then when \(x = -2\), \(f(x)\) should equal zero.

Step 3 ：We can substitute \(x = -2\) into the function \(f(x) = kx + 6\) and solve for k.

Step 4 ：Substituting \(x = -2\) into the function \(f(x) = kx + 6\) gives us the equation \(6 - 2k = 0\).

Step 5 ：Solving this equation for k gives us \(k = 3\).

Step 6 ：Final Answer: The value of k is \(\boxed{3}\).