Question

Factor the polynomial given a common factor.

Answer 1

The answer that goes in the blank is x-pi/2

Where the "-pi/2" part is its own fraction (x is not part of it; i.e., x is not in the numerator of the fraction). 

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To find this answer, we need to ask ourselves: "1/3 times what quantity will give us (1/3)x?". The answer to this sub-question is simply x. In other words, 1/3 times x is (1/3)x. That takes care of the first part.

For the second part, we have 1/3 times something equal to -pi/6. That "something" must be -pi/2. Note how

(1/3)*(-pi/2) = (1*(-pi))/(3*2) = -pi/6

So you have to think backwards in a sense. Or you can treat it like this

(1/3)*y = -pi/6

Multiplying both sides by 3 leads to 

y = -pi/2

Answer 2

if you have the polynomial $\frac{1}{3}$ x - $\frac{ \pi}{6}$ by factoring out $\frac{1}{3}$ then the result would be:

$\frac{1}{3}$ x   -   $\frac{ \pi}{6}$  =   $\frac{1}{3}$  [($\frac{1}{3}$ ÷ $\frac{1}{3}$ x) - ($\frac{ \pi}{6}$ ÷ $\frac{1}{3}$ )]

                                   = $\frac{1}{3}$ ( x - $\frac{ \pi}{2}$)