Answer: You have the correct answer. It's choice A.
Step-by-step explanation:
You can verify this by plugging each root into the equation.
So for instance, plug in x = -2 and we get
f(x) = -3*(x+2)*(x-sqrt(3))*(x-4)
f(-2) = -3*(-2+2)*(-2-sqrt(3))*(-2-4)
f(-2) = -3*(0)*(-2-sqrt(3))*(-2-4)
f(-2) = 0
This verifies x = -2 is a root.
All that matters is that zero buried in there in the second to last step. Multiplying 0 by anything leads to 0. The other roots are verified in the same manner. The -3 out front is the leading coefficient.
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Extra info:
- Choice B is eliminated because (x+3) being a factor implies that x = -3 is a root. But this isn't listed in the instructions.
- Choice C is a similar story to choice B
- Choice D is eliminated since -sqrt(3) is not one of the listed roots, so (x+sqrt(3)) is not a factor.