Question

Which of the following is a polynomial?

Answer 1

Answer:

D

Step-by-step explanation:

Terms are separated by addition and subtraction symbols.

Polynomials consist of terms that are constant and/or variable. The variable terms must have 0 or positive exponents. Polynomials will not consist of division of variable expressions.

Examples of polynomials:

$5$

$5x$

$6-x$

$24x^9-x$

Examples of non-polynomials:

$\sqrt{x}$

$\frac{x+2}{x-4}$

In general a polynomial when written in standard form should be comparable to:

$a_nx^n+a_{n-1}x^{n-1}+\cdots a_3x^3+a_2x^2+a_1x+a_0$

where the $a$'s could be zero and all the exponents,n, are positive or 0.

D is comparable since all of these are 0 except $x_4$ which is 1 and $x_0$ which is -2.

Also the other choices have either division by variable expressions and/or negative exponents on variables.