Saying "3x-2 is a factor of f(x)" means that
f(x) = (3x-2)*p(x)
where p(x) is some other polynomial
If we set f(x) equal to zero and use the zero product property, then we know that 3x-2 = 0 and p(x) = 0
Solve 3x-2 = 0 for x to get x = 2/3
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In short, if we plugged x = 2/3 into the original f(x) function, we would get zero.
So the idea is you plug x = 2/3 into 3x^3 - 5x^2 + k*x + 2 and set that equal to zero, and solve for k
3x^3 - 5x^2 + k*x + 2 = 0
3(2/3)^3 - 5(2/3) + k*(2/3) + 2 = 0
3(8/27) - 5(2/3) + (2/3)k + 2 = 0
I'll let you finish up. If you're still stuck, then please let me know. Thank you.
