5x^2+10x^1-3x+2 is the polynomial in standard form. Explain the closure property as it relates to polynomials. Give an example.

each term of the polynomial is also a polynomial.

polynomials are closed under addition.

Did you know?

A polynomial in standard form, such as 5x^2+10x^1-3x+2, is written with the terms arranged in descending order by the exponent. The closure property of polynomials states that when two polynomials are added, subtracted, or multiplied together, the result will always be another polynomial. This means that the set of polynomials is closed under these operations. For example, if we have the polynomials P(x) = 3x^2 + 4x - 1 and Q(x) = 2x^3 + 5x^2 - 2x + 3, we can add them together to obtain R(x) = P(x) + Q(x) = 2x^3 + 8x^2 + 2x + 2. Notice how the result is also a polynomial. This closure property is important in algebraic operations involving polynomials, as it guarantees that combining or manipulating polynomials will always yield another polynomial.