What os the domain of the given function

Factorize: x^2+8x+10 i just solved it but i don't know if the process is correct

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

How is the equation of this circle written in standard form? x2 + y2 - 6x + 14y = 142 a) (x - 3)2 + (y + 7)2 = 200 b) (x+ 3)2 + (y - 7)2 = 200 (x - 6)2 + (y + 14)2 = 142 d) (x+6)2 + (y- 14)2 = 142