Use the following multiplication problem to show how multiplying polynomials is a closed system.
(x2 −3)(−3x + 7)
To show that multiplying polynomials is a closed system, we need to multiply the given polynomials and demonstrate that the result is also a polynomial.
Multiplying (x^2 - 3) by (-3x + 7):
(x^2 - 3) * (-3x + 7) = x^2 * (-3x) + x^2 * 7 + (-3) * (-3x) + (-3) * 7
= -3x^3 + 7x^2 + 9x - 21
As we can see, the result is a polynomial (-3x^3 + 7x^2 + 9x - 21), which means that the product of two polynomials is itself a polynomial. Therefore, multiplying polynomials is a closed system.