Question

Integers and polynomials are both _[blank 1]_ under addition, subtraction, and multiplication; however, operations on polynomials _[blank 2]_ while operations on integers _[blank 3]_.

Answer 1

Integers and polynomials are both closed under addition, subtraction, and multiplication; however, operations on polynomials can sometimes be open while operations on integers produce irrational results .

Explanation:

Closed means that addition, subtraction, and multiplication of integers gives as result a new integer; and addition, subtraction, and multiplication of polynomials gives as result a new polynomial.

Operations on polynomials can sometimes be open, like in division.

Operations on integers can produce irrational results , for example, dividing 11 by 9.