Question

You don’t need to do it just explain the process of 10 please

Answer 1

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.