Question

Show how multiplying polynomials is closed system (x^2-1)(-2x+5)

Answer 1

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.