Answer:
The following expressions are polynomials:
[tex]3x^2-5x^4+2x-12[/tex]
[tex]x^5-5x^4+4x^3-3x^2+2x-1[/tex]
[tex]x^3-7x^2+9x-5x^4-20[/tex]
The following expressions are not polynomials:
[tex]\frac{4}{x^4}+\frac{3}{x^3}-\frac{2}{x^2}-1[/tex]
[tex]x^{-5}-5x^{-4}+4x^{-3}-3x^{-2}+2x^{-1}-1[/tex]
[tex]\sqrt[4]{x}-\sqrt[3]{x}+4\sqrt{x}-8x+16[/tex]
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, [tex]a_{n}x^{n}+a_{n-1}x^{n-1}+.....+a_{1}x+a_{0}[/tex], with 'n' being non-negative integer.
Thus, according to the definition, we have that,
The following expressions are polynomials:
[tex]3x^2-5x^4+2x-12[/tex]
[tex]x^5-5x^4+4x^3-3x^2+2x-1[/tex]
[tex]x^3-7x^2+9x-5x^4-20[/tex]
The following expressions are not polynomials:
[tex]\frac{4}{x^4}+\frac{3}{x^3}-\frac{2}{x^2}-1[/tex]
[tex]x^{-5}-5x^{-4}+4x^{-3}-3x^{-2}+2x^{-1}-1[/tex]
[tex]\sqrt[4]{x}-\sqrt[3]{x}+4\sqrt{x}-8x+16[/tex]
