Does the line have to go through the x-axis to be called a distinctive x-intercept or does just touching the x-axis enough to be called an x-intercept? i. e. for this equation y=(x+2)^2(x+1)(x-1)(x-2)^2 what is the product of the distinct x-intercepts?

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.