Question

Use the following multiplication problem to show how multiplying polynomials is a closed system.

(x²−1)(−2x 5)

Answer 1

Multiplying polynomials is a closed system. When we multiply two polynomials, the product will also be a polynomial.

Step-by-step explanation:

Multiplying polynomials is a closed system, which means that when we multiply two polynomials, the product will also be a polynomial. Let's use the given multiplication problem as an example: (x²−1)(−2x+5).

To multiply these polynomials, we use the distributive property. We multiply each term in the first polynomial by each term in the second polynomial:

• (x²)(-2x) = -2x³
• (x²)(5) = 5x²
• (-1)(-2x) = 2x
• (-1)(5) = -5

Now we combine like terms by adding or subtracting:

• -2x³ + 5x² + 2x - 5

Therefore, the product of (x²−1)(−2x+5) is -2x³ + 5x² + 2x - 5, which is a polynomial.