Integer-valued polynomial
Okay kiddo, so imagine you have a bunch of numbers, like 1, 2, 3, 4, 5, and so on. These are called integers.
Now, let's talk about polynomials. It's like a math problem that has letters and numbers in it. For example, x + 2 is a polynomial. We can substitute a number in for x, like 3, and get an answer: 3 + 2 = 5.
But sometimes we want to know if the answer will be an integer, which is just a fancy way of saying a whole number with no fractions or decimals. And that's where an integer-valued polynomial comes in.
An integer-valued polynomial is just a special kind of polynomial where if we put in any integer (remember, those are the whole numbers with no fractions or decimals), we'll get an integer as the answer too. So if we put in 2 for x in the polynomial x^2 + 2x + 1, we get 2^2 + 2(2) + 1 = 9, which is also an integer!
So basically, an integer-valued polynomial is just a type of math problem that always gives you a whole number answer no matter what whole number you put into it.
Now, let's talk about polynomials. It's like a math problem that has letters and numbers in it. For example, x + 2 is a polynomial. We can substitute a number in for x, like 3, and get an answer: 3 + 2 = 5.
But sometimes we want to know if the answer will be an integer, which is just a fancy way of saying a whole number with no fractions or decimals. And that's where an integer-valued polynomial comes in.
An integer-valued polynomial is just a special kind of polynomial where if we put in any integer (remember, those are the whole numbers with no fractions or decimals), we'll get an integer as the answer too. So if we put in 2 for x in the polynomial x^2 + 2x + 1, we get 2^2 + 2(2) + 1 = 9, which is also an integer!
So basically, an integer-valued polynomial is just a type of math problem that always gives you a whole number answer no matter what whole number you put into it.