Question

Simplify the expression.

Then, in 1–2 sentences, explain how multiplying polynomials is a closed system.

(x2−1)(−2x+5)

(2 points)

Answer 1

(x^2 − 1)(−2x + 5) = −2x^3 + 5x^2 + 2x − 5.

Multiplying polynomials is closed because distributing terms produces a finite sum of powers of x with coefficients from the same number set, so the product is again a polynomial (its degree is at most the sum of the degrees).