Question

I am desperate 98 point for the person who answers this right Polynomials are a close/not closed system under addition and subtraction as are whole numbers and integers/all number/monomial/whole number. When you add or subtract polynomials you end up with other polynomial/whole number/integers/binomials.

Answer 1

Polynomials form a closed system under both addition and subtraction, meaning the result will always be another polynomial. The basic principle is combining like terms, observing the order of operations and the signs of coefficients.

Step-by-step explanation:

Polynomials are a closed system under addition and subtraction, just as whole numbers and integers are. This means that when you add or subtract polynomials, the result is always another polynomial. The basic principle in working with addition and subtraction is to combine like terms while paying attention to the signs of the coefficients. When working specifically with whole numbers, you pay attention to maintaining the properties of closure, commutativity (e.g. A + B = B + A), and associativity.

As an example, when adding the polynomials (2x2 + 3x + 1) and (x2 - 4x + 5), you combine like terms to get another polynomial: 3x2 - x + 6. Similarly, subtracting (x - 3) from (2x2 + x + 1) results in the polynomial 2x2 - 2. The resulting expressions following these operations remain as polynomials, not turning into integers or any other type of number.

Answer 2

The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Consequently, polynomials are closed under multiplication. Polynomials are NOT closed under division.

Step-by-step explanation:

Example

What's the degree of the following polynomials?

x2+x

The first monomial has a degree of 2 and the second monomial has a degree of 1. The highest degree is 2 which mean that the degree of the polynomial is 2.

x4+x2+x

4, 2 and 1 , the highest degree is 4 which mean that the degree of the polynomial is 4.

We can add and subtract polynomials. We just add or subtract the like terms to combine the two polynomials into one.