Question

Which of the following expressions is not a polynomial?

• A. $6y^3+5y^2-2y-9$
• B. $-\frac{2}{9}{x}^{2}y+\frac{4}{13}{x}^2{y}^2+6y^3$
• C. $(a^3-8a)(x^4+6)$
• D. $\frac{5x^4+7x^2{y}^2-8}{y}$

Answer 1

The correct option is D $\frac{5x^4+7x^2{y}^2-8}{y}$

A Polynomial can be expressed in terms that only have positive integer exponents and the operations of addition, subtraction, and multiplication. In other words, it must be possible to write the expression without division.

$\left(A\right)6y^3+5y^2-2y-9$

Since all of the variables have integer exponents that are positive this is a polynomial.

$\left(B\right)-\frac{2}{9}{x}^{2}y+\frac{4}{13}{x}^2{y}^2+6y^2$

Since all of the variables have integer exponents that are positive this is a polynomial.

$\left(C\right)(a^3-8a)(x^2+6)$

Since all of the variables have integer exponents that are positive this is a polynomial.

$\left(D\right)\frac{5x^2+7x^2{y}^2-8}{y}=\frac{5x^2}{y}+\frac{7x^2{y}^2}{y}-\frac{8}{y}=5x^2{y}^{-1}+7x^{2}y-8y^{-1}$

Not a polynomial because of the division

Then (D) is not polynomial