Given the function f(x) = 1 + 2x3, find the value of f() in simplest form.

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?

Kevin's bank offered him a 4.5% interest rate for his mortgage. if he purchases 3 points, what will be his new rate?

Simplify. 3(4+4x) (type your answer in with no spaces)