To find the quotient of the polynomial \( 20t^4 - 12t^3 + 8t^2 \) divided by \( 4t^2 \), we can perform polynomial long division or simply simplify by dividing each term by \( 4t^2 \).
Starting with the polynomial \( 20t^4 - 12t^3 + 8t^2 \):
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Divide each term by \( 4t^2 \):
\[ \frac{20t^4}{4t^2} = 5t^2 \] \[ \frac{-12t^3}{4t^2} = -3t \] \[ \frac{8t^2}{4t^2} = 2 \]
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Now, combine these results:
\[ 5t^2 - 3t + 2 \]
Thus, the quotient of \( 20t^4 - 12t^3 + 8t^2 \) divided by \( 4t^2 \) is:
\[ \boxed{5t^2 - 3t + 2} \]