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

Question

Mathematics

Hazel Williams

11 June, 16:51

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

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Julius · 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.

Step-by-step 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.