SOLUTION: A student states that polynomials are closed under division. Which of the following expressions are counterexamples to the statement?
Choose all answers that are correct.
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-> SOLUTION: A student states that polynomials are closed under division. Which of the following expressions are counterexamples to the statement?
Choose all answers that are correct.
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Question 934535: A student states that polynomials are closed under division. Which of the following expressions are counterexamples to the statement?
Choose all answers that are correct.
__ x^3 ÷ x^6
__ x^6 ÷ 3x^2
__ (x^4 – 121) ÷ (x – 121)
__ (x^2 – 6x + 9) ÷ (x – 3) Answer by Theo(13342) (Show Source):
a polynomial must have all variables raised to a non-negative integer.
x^3/x^6 = x^-3 which is not a polynomial because the exponent of the variable is negative.
(x^6) / (3x^2) = (x^4)/3 which is a polynomial because the exponent of the variable is a non-negative integer.
(x^4 - 121) / (x - 121) results in x^3 + 121x^2 + 121^2x + 121^3 + (121^4-121)/(x-121) which is not a polynomial because the last term has the variable being raised to a negative exponent because 1/(x-121) = (x-121)^-1.
(x^2 - 6x + 9) / (x-3) results in (x-3) which is a polynomial because the exponent of the variable is a non-negative integer.
looks like the first one and the third one are counter examples because the result of those operations is not a polynomial.
here's some examples of expressions that are polynomial and expressions that are not polynomial.
