Question

Multiplying polynomials is a closed system because the product of any two polynomials (which are defined as sums of terms with non-negative integer exponents) will always yield another polynomial, meaning the set of polynomials is closed under multiplication.

Rewrite in a 6 th graders response

Answer 1

Multiplying polynomials is like a special math rule that works every time. When you take two polynomials (which are just sums of terms with whole number powers of x, like \(x^2 + 3x + 1\)), and you multiply them together, you always get another polynomial. So, you can keep multiplying polynomials, and you’ll always end up with a polynomial. That’s why we say that polynomials are "closed" under multiplication!