The polynomials are:
[tex]x^4+3x^3-5x^2-7x+20[/tex]
[tex]x^3-2x^2+x-12[/tex]
[tex]x^2+3x^5-6x+12x^3[/tex]
Not a polynomial are:
[tex]4\sqrt[3]{x} -\sqrt{x} -20[/tex]
[tex]\frac{5}{x^3}-\frac{1}{x^2}+\frac{8}{x}-40[/tex]
[tex]x^{-3}-x^{-2}-6x^{-1}+8[/tex]
Solution:
Polynomial is an expression with variables and coefficients,
Which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables
Option 1
[tex]4\sqrt[3]{x} -\sqrt{x} -20[/tex]
Polynomial does not include roots
This is not a polynomial equation
Option 2
[tex]x^4+3x^3-5x^2-7x+20[/tex]
This is polynomial expression involving addition and subtraction between terms with non-negative integer exponents of variables
Option 3
[tex]\frac{5}{x^3}-\frac{1}{x^2}+\frac{8}{x}-40[/tex]
This is not a polynomial. This equations involves negative integer exponents of variables
Option 4
[tex]x^3-2x^2+x-12[/tex]
This is a polynomial involving addition and subtraction between terms with non-negative integer exponents of variables
Option 5
[tex]x^{-3}-x^{-2}-6x^{-1}+8[/tex]
This is not a polynomial. This equations involves negative integer exponents of variables
Option 6
[tex]x^2+3x^5-6x+12x^3[/tex]
This is a polynomial involving addition and subtraction between terms with non-negative integer exponents of variables
