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dwh2o13
Looks like you answer will be choice A...

Now why are the others not???
B. this is the product of two polynomials
C. this looks like a polynomial but notice the second term..it has a negative exponent. Exponents have to be of the set 0,1,2,3....
D. this expression introduces division by a variable which cannot happen in polynomials....note the first term where x is raised to the exponent of "-x"
BladeRunner212

x² + 2

Further explanation

Let us determine whether each algebraic expression is a polynomial or not.

  • [tex]\boxed{ \ A. \ x^2 + 2 \ }.[/tex] is a polynomial.
  • [tex]\boxed{ \ B. (x^8 - 2)/(x^{-2} + 3) \rightarrow \frac{(x^8 - 2)}{(x^{-2} + 3)} \ }[/tex] is not a polynomial, but a rational function.
  • [tex]\boxed{ \ C. \ 7x^7 - 2x^{-4} + 3 \ }[/tex] is not a polynomial, because - 4 is not a whole number power.
  • [tex]\boxed{ \ D. \ x^{-x} - 1 \ }[/tex] is not a polynomial, because - x is not a power of integer but a variable as well.

Let us rephrase the following definitions.

  • A monomial is an algebraic expression which comprises a single real number, or the product of a real number and one or more variables raised to whole number powers. For example, [tex]\boxed{-2} \boxed{3x^2} \boxed{4a^3b^4} \boxed{-5xy^3z^2} \boxed{\frac{3}{5}}[/tex]
  • A coefficient is each real number preceeding the variable(s) in a monomial. In the examples above [tex]\boxed{ \ -2, 3, 4, -5, \frac{3}{5} \ }[/tex] are the coefficients.
  • A polynomial is the sum or difference of a set of monomials. For example, [tex]\boxed{ \ 2x^2 - 3xy^2 + 4x^2y \ }[/tex]
  • Each monomial that forms a polynomial is called a term of that polynomial. For example, the term of polynomial [tex]\boxed{ \ 2x^2 - 3xy^2 + 4x^2y \ }[/tex] are [tex]\boxed{ \ 2, - 3, and \ 4. \ }[/tex]
  • The constant term is the term of polynomial that does not contain a variable.
  • The leading coefficient is the coefficient of the term containing the variable raised to the highest power.

For example, consider the polynomial [tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex]

  • [tex]\boxed{ \ 2x^4, - 3x^2, - 4x, and \ - 5 \ }[/tex] are the terms of polynomial.
  • [tex]\boxed{ \ 2, - 3, - 4 \ }[/tex] are the coefficients.
  • - 5 is the constant term.
  • 2 is the leading coefficient.

A polynomial is said to be in standard form if the terms are written in descending order of degree. For example:

  • [tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex] is a polynomial in standard form.
  • [tex]\boxed{ \ - 3x^2 + 2x^4 - 5- 4x \ }[/tex] is the polynomial, but it is not in standard form.

Learn more

  1. The remainder theorem https://brainly.com/question/9500387
  2. 68.32 divided by 2.8 is divisible https://brainly.com/question/5022643#
  3. Which expression is equivalent to the product of a binomial and a trinomial after it has been fully simplified https://brainly.com/question/1394854

Keywords: which of the following is a polynomial, a monomial, terms, the leading coefficient, constant, in a standard form, rational function, whole number power, integer

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