Question

Which of the following are polynomials?

A. x^2 + x + 1/x^2 + 1
B. 2/x^3 + x + 1/2
C. 2/3x^2 + x + 1
D. x^2/3 + 0x + 1
E. x^3 + 2x + square root of 2

Answer 1

Explanation:

Answer 2

The polynomials are:

`(2)/(3)` x² + x + 1 ⇒ C

x³ + 2x +√2 ⇒ E

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 ⇒ (
`(1)/(x^(2)+1 )` ,
`(2)/(x^(3))` )

∴ Answers A and B are not polynomials

∵ The polynomial has integer exponents of variables

∵ Answer D has a fraction exponent of x ⇒
`x^{(2)/(3)}`

∴ Answer D is not a polynomial

∵
`(2)/(3)` x² + x + 1 has a non-negative integer exponent of x

∵ There is no division by x

∴
`(2)/(3)` 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
`(2)/(3)` x² + x + 1 and x³ + 2x +√2