Answer:
The polynomials are:
[tex]\frac{2}{3}[/tex] x² + x + 1 ⇒ C
x³ + 2x +√2 ⇒ E
Step-by-step explanation:
A polynomial: is an expression consisting of variables and coefficients, with the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables
- A polynomial never division by a variable
- A polynomial could be one term, and it could be just a constant
Let us solve the question
∵ The polynomial never division by a variable
∵ Answer A and B have a division in variable ⇒ ( [tex]\frac{1}{x^{2}+1 }[/tex] , [tex]\frac{2}{x^{3}}[/tex] )
∴ Answers A and B are not polynomials
∵ The polynomial has integer exponents of variables
∵ Answer D has a fraction exponent of x ⇒ [tex]x^{\frac{2}{3}}[/tex]
∴ Answer D is not a polynomial
∵ [tex]\frac{2}{3}[/tex] x² + x + 1 has a non-negative integer exponent of x
∵ There is no division by x
∴ [tex]\frac{2}{3}[/tex] x² + x + 1 is a polynomial
∵ x³ + 2x +√2 has a non-negative integer exponent of x
∵ There is no division by x
∴ x³ + 2x +√2 is a polynomial
∴ The polynomials are [tex]\frac{2}{3}[/tex] x² + x + 1 and x³ + 2x +√2
