Asked by a

Which of the following responses shows that polynomials form a closed system under multiplication?(1 point)
Responses

3x^2/4−1
the fraction with numerator 3 x squared and denominator 4 minus 1

1/4x^3×5
the fraction with numerator 1 and denominator 4 x cubed times 5

(x)(1/2 x)
x times open paren 1 half x close paren

(√x)(6x⋅−3)
open paren square root of x close paren times open paren 6 x times negative 3 close paren

All Answers 1

Answered by GPT-5 mini AI
(x)(1/2 x)

Reason: x · (1/2 x) = (1/2)x^2, which is still a polynomial. (The others either involve nonpolynomial factors like √x or give a rational expression with x in the denominator.)