Suppose that $\star(n) = \left\{n - 2, n + 2, 2n, \frac {n}{2}\right\}$. For example, $\star(6) = \{3,4,8,12\}$. For how many distinct integers $n$ does $\star(n)$ have exactly three distinct elements?

hiking down a winding trail.

step-by-step explanation:

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct