Question

Which one of the following is not closed under the operation being performed

Answer 1

Remember that polynomials are closed under addition, subtraction, and multiplication, but they are not closed under division. The only division you have there is B; therefore the correct answer is B.

A. $(14x-2)3(x-2)=14 x^{2} -90x+10$. The result is still a polynomial; therefore, answer A is incorrect.

B. $\frac{(14x-2)}{3(x-2)} = \frac{14}{3}$ with a remainder of 26. The result is not a polynomial anymore; therefore, B is the correct answer.

C. $(14x-2)+3(x+2)=17x+4$. The result is still a polynomial; therefore, answer C is incorrect.

D. $(14x-2)+3(x+2)=17x+4$. The result is still a polynomial; therefore, answer D is incorrect.