How do you find

  use an appropriate calculator

Step-by-step explanation:

You didn't ask the value; you only asked how to find the value. Here is an answer for that question.

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If your calculator does not have a cube-root function, you can use a 1/3 power:

 

Alternatively, you can use logarithms:

 

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The Google calculator recognizes the cube root( ) function as shown in the attachment.

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Since you know 6^3 = 216, you know the cube root of 219 is only a little more than 6. A couple of iterations of ...

  x' = (2/3)x +73/x^2

can refine your first guess of x=6 to 8 decimal places of accuracy, where x' is the next "guess". One more iteration will give the cube root to the accuracy displayed by most calculators.

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In the above iteration formula, the value 73 is 219/3. This same sort of iterative technique can be used for any cube root. It calculates the next guess as the weighted average: 2/3 of the previous guess and 1/3 of the number divided by the square of the guess. Once you're in the ballpark, it will double the number of accurate decimal digits on each iteration.

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The correct answer is that 3x²-11x+8 will be a polynomial.

Explanation:
When we subtract polynomials, we combine like terms:
3x² is the only x² term we have.
We have -6x and subtract 5x from it; this gives us -11x.
We have 2 and subtract -6 from it; when we subtract a negative, we add the opposite, which means we have 2--6=2+6=8.

This gives us 3x²-11x+8. This is a polynomial, since it is made of monomials (none of the terms have a negative exponent or a radical sign).