Question

Factor the polynomial given a common factor.

Answer 1

if you have the polynomial
`(1)/(3)` x -
`( \pi)/(6)` by factoring out
`(1)/(3)` then the result would be:


`(1)/(3)` x -
`( \pi)/(6)` =
`(1)/(3)` [(
`(1)/(3)` ÷
`(1)/(3)` x) - (
`( \pi)/(6)` ÷
`(1)/(3)` )]

=
`(1)/(3)` ( x -
`( \pi)/(2)`)

Answer 2

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).

-------------------------------------

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