To divide the polynomial \( 20x^4 - 12x^3 + 10x^2 + 3x - 16 \) by \( -4x^2 + 2 \), we proceed with polynomial division.
Given the result of the division, the quotient is:
[tex]\[ -5x^2 + 3x - 5 \][/tex]
And the remainder is:
[tex]\[ -3x - 6 \][/tex]
Thus, the division expression can be written as:
[tex]\[
\frac{20x^4 - 12x^3 + 10x^2 + 3x - 16}{-4x^2 + 2} = -5x^2 + 3x - 5 + \frac{-3x - 6}{-4x^2 + 2}
\][/tex]
So, our final result in the required form is:
[tex]\[ \boxed{-5x^2 + 3x - 5 + \frac{-3x - 6}{-4x^2 + 2}} \][/tex]
