Which of the following options correctly describes if the following polynomial forms a closed system under multiplication?
−3(5x+4y)=−15/x−12y
None of the options correctly describe if the polynomial forms a closed system under multiplication.
To determine if a polynomial forms a closed system under multiplication, we need to check if multiplying two polynomials of the given form results in another polynomial of the same form.
The given polynomial is −3(5x+4y) = −15/x−12y.
To check if it is closed under multiplication, we will multiply the polynomial by a second polynomial.
Let's choose another polynomial (a+bx+cy) and multiply it by the given polynomial:
(−3)(5x+4y)(a+bx+cy)=(−3)(5a+4b)(x+ay+cy) = −15a−12b(x+ay+cy) = −15a−12bx−12c(y)−12ay−12bxy−12c(y^2)
After multiplying the two polynomials, we obtained a polynomial of the same form: −15a−12bx−12c(y)−12ay−12bxy−12c(y^2).
Therefore, the given polynomial form is closed under multiplication.