To show that multiplying polynomials is a closed system, we need to demonstrate that the result of multiplying two polynomials is also a polynomial.
Given the multiplication problem (x^2−1)(−2x+5), we can expand it using the distributive property:
(x^2)(-2x) + (x^2)(5) + (-1)(-2x) + (-1)(5)
Simplifying this expression:
-2x^3 + 5x^2 + 2x - 5
The result of multiplying the two polynomials is -2x^3 + 5x^2 + 2x - 5, which is a polynomial. Therefore, multiplying polynomials is a closed system.
Use the following multiplication problem to show how multiplying polynomials is a closed system.
(x2−1)(−2x+5)
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