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Which of the following are polynomials?
(Select all that apply)
A
(1)/(2)x^(2)+7x+4
B
x^(-2)+23 x-99
C
5x^(2)-12 x
D
(1)/(x^(2))+5x-12

Which of the following are polynomials? $\newline$ (Select all that apply) $\newline$ A $\frac{1}{2} x^{2}+7 x+4$ $\newline$ B $x^{-2}+23 x-99$ $\newline$ C $5 x^{2}-12 x$ $\newline$ D $\frac{1}{x^{2}}+5 x-12$

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Simplify rational expressions

Full solution

Q. Which of the following are polynomials?

\newline

(Select all that apply)

\newline

A

\frac{1}{2} x^{2}+7 x+4

\newline

B

x^{-2}+23 x-99

\newline

C

5 x^{2}-12 x

\newline

D

\frac{1}{x^{2}}+5 x-12

Define Polynomial: Identify the definition of a polynomial: A polynomial is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
Option A Analysis: Analyze option A: $(\frac{1}{2})x^2 + 7x + 4$ . All terms have non-negative integer exponents and involve allowed operations.
Option B Analysis: Analyze option B: $x^{-2} + 23x - 99$ . The term $x^{-2}$ has a negative exponent, which is not allowed in polynomials.
Option C Analysis: Analyze option C: $5x^2 - 12x$ . All terms have non-negative integer exponents and involve allowed operations.
Option D Analysis: Analyze option D: $\frac{1}{x^2} + 5x - 12$ . The term $\frac{1}{x^2}$ can be rewritten as $x^{-2}$ , which has a negative exponent, not allowed in polynomials.

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