T^T i suck at mathfree points

Which of the following is true for the relation f(x)=2x^2+1

In the polynomial below, what number should replace the question mark to produce a difference of squares? x2 + ? x - 36

1- 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.2- 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 the first question?