Algebra-1

The domain of any polynomial function is all real numbers.

For the range, we note that we can rewrite the function as y = -x²(2x⁴ - 5x² + 3).

Let t = x², then the function becomes y = -t(2t² - 5t + 3).

Since t = x² ≥ 0 and the leading coefficient of the polynomial in t is negative, the function has a maximum value at the vertex of the parabola.

Completing the square or using the vertex formula shows that the function is always less than or equal to 0, so the range is 

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