For a polynomial P(x), the quotient P(x)/(x-2) has a remainder of 12. What is the value of P(2)? Please explain. Thanks :)

12

Step-by-step explanation:

P(x) has infinitely many solutions, but I am going to find the easiest one, which would be a linear equation.

First, notice that x-2 perfectly divides into itself.

Then, if you add 12 to x-2, you will end up with a remainder of 12. Therefore, P(x) would be x-2+12 = x+10.

Now that we know P(x), we can directly plugin 2 to find out P(2):

2+10 = 12

Therefore, P(2) = 12.