Question

HELP QUICK TIMED!!!!!!Drag the expressions into the boxes to correctly complete the table.

Answer 1

Answer:

The following expressions are polynomials:

$3x^2-5x^4+2x-12$

$x^5-5x^4+4x^3-3x^2+2x-1$

$x^3-7x^2+9x-5x^4-20$

The following expressions are not polynomials:

$\frac{4}{x^4}+\frac{3}{x^3}-\frac{2}{x^2}-1$

$x^{-5}-5x^{-4}+4x^{-3}-3x^{-2}+2x^{-1}-1$

$\sqrt[4]{x}-\sqrt[3]{x}+4\sqrt{x}-8x+16$

Step-by-step explanation:

We are required to differentiate the expressions as polynomials and non-polynomials.

Since, we know,

A polynomial is an expression that involves variables and their coefficients separated by mathematical operations with the variables having non-negative integer values.

i.e. A polynomial is of the form, $a_{n}x^{n}+a_{n-1}x^{n-1}+.....+a_{1}x+a_{0}$, with 'n' being non-negative integer.

Thus, according to the definition, we have that,

The following expressions are polynomials:

$3x^2-5x^4+2x-12$

$x^5-5x^4+4x^3-3x^2+2x-1$

$x^3-7x^2+9x-5x^4-20$

The following expressions are not polynomials:

$\frac{4}{x^4}+\frac{3}{x^3}-\frac{2}{x^2}-1$

$x^{-5}-5x^{-4}+4x^{-3}-3x^{-2}+2x^{-1}-1$

$\sqrt[4]{x}-\sqrt[3]{x}+4\sqrt{x}-8x+16$

Answer 2

To qualify as a polynomial, the expression in question:
* Consists of one or more terms 
* Variables are only with positive whole exponents
* No variables in the denominator of any term.