Quadratics: Factoring and Solving Quadratics Using FOIL

If $$(x-2\sqrt{3})$$ is one factor of the quadratic $$x^2+(4\sqrt3)x-36$$, what is the other factor?

Correct. [[snippet]] Since $$(x-2\sqrt{3})$$ is a factor, you know that $$e = -2\sqrt{3}$$. _(Of course, it could be the case that $$f = -2\sqrt{3}$$, but $$e$$ and $$f$$ are interchangeable, so it doesn't matter which one you assign to the known value.)_ In the given quadratic, you can see that $$b$$, the coefficient of the $$x$$-term, is $$4\sqrt{3}$$. That gives you the equation: > $$e+f = b$$ > $$-2\sqrt3 + f = 4\sqrt3$$. Adding $$2\sqrt{3}$$ to both sides gives > $$f = 6\sqrt3$$. Thus, the other factor is $$x+f = x+6\sqrt3$$.

Incorrect. [[snippet]] Make sure you find a factor so that $$e+f = 4\sqrt{3}$$.

Incorrect. [[snippet]] Carefully check your calculations.

Incorrect. [[snippet]] You might have gotten this answer if you made a sign error.

Incorrect. [[snippet]] You need to find a factor so that $$e+f = 4\sqrt{3}$$.

$$x+2\sqrt{3}$$

$$x+4\sqrt{3}$$

$$x+6\sqrt{3}$$

$$x-2\sqrt{3}$$

$$x-6\sqrt{3}$$