To show that multiplying polynomials is a closed system, we need to demonstrate that when we multiply two polynomials, the result is also a polynomial.
Let's multiply the given polynomials:
(x^2 - 1)(-2x + 5)
First, distribute the terms:
-2x(x^2 - 1) + 5(x^2 - 1)
Now, multiply each term:
-2x * x^2 + (-2x) * (-1) + 5 * x^2 + 5 * (-1)
Simplify:
-2x^3 + 2x + 5x^2 - 5
Now, combine like terms:
-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, we have shown that multiplying polynomials is a closed system.
Show how multiplying polynomials is closed system (x^2-1)(-2x+5)
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