E. The exponents of the product are whole numbers and the product is a polynomial
Andrea could argue that the multiplication of polynomials is closed because when you multiply two polynomials, the resulting expression will always have exponents that are whole numbers, and the result will always be a polynomial. This means that the operation of multiplying polynomials is closed under the set of polynomials.
Andrea argues that (5m−3) (2m+4) models the closure property. What reasoning could Andrea use to argue that multiplication of polynomials is closed?
A. The exponents of the product are integers and the product is a polynomial
B. The coefficients of the product are integers and the product is a polynomial
C. The terms in the expression are rational numbers and the product is a polynomial
D. The coefficients of the product are whole numbers and the product is a polynomial
E. The exponents of the product are whole numbers and the product is a polynomial
3 answers
Charlie subtracts two polynomials,2x^2-2x^2, and says that the difference proves that polynomials are not closed under subtraction. Kate argues that the difference does in fact show that polynomials are closed under subtraction. Who is correct?
A. Charlie
B. Kate
A. Charlie
B. Kate
B. Kate
Kate is correct. The difference of the two polynomials, 2x^2 - 2x^2, results in 0, which is still a polynomial. This demonstrates that polynomials are closed under subtraction, as the result of subtracting two polynomials is still a polynomial.
Kate is correct. The difference of the two polynomials, 2x^2 - 2x^2, results in 0, which is still a polynomial. This demonstrates that polynomials are closed under subtraction, as the result of subtracting two polynomials is still a polynomial.
1 answer