Final answer:
The closure property of polynomials states that the sum of two polynomials will always result in another polynomial, which is demonstrated by adding two polynomials together to get a new polynomial.
Step-by-step explanation:
The closure property states that the sum of two polynomials is a polynomial. This means that when you add two polynomials together, the result will also be a polynomial.
To exemplify, consider two polynomials P(x) and Q(x).
If P(x) = 2x^2 + 3x + 1 and
Q(x) = 5x^2 - 4x + 3, adding them gives you a new polynomial
R(x) = (2x^2 + 3x + 1) + (5x^2 - 4x + 3),
which simplifies to R(x) = 7x^2 - x + 4.
The result, R(x), is still a polynomial, thus demonstrating the closure property of polynomials with respect to addition.