Calculate the quotient of the polynomial \( 4x^4 - 8x^3 + 6x^2 \) divided by \( 2x^2 \).

To find the quotient of the polynomial \( 4x^4 - 8x^3 + 6x^2 \) divided by \( 2x^2 \), we need to divide each term of the polynomial by \( 2x^2 \). 1. Divide the first term: \[ \frac{4x^4}{2x^2} = 2x^{4-2} = 2x^2 \] 2. Divide the second term: \[ \frac{-8x^3}{2x^2} = -4x^{3-2} = -4x \] 3. Divide the third term: \[ \frac{6x^2}{2x^2} = 3 \] Now, we combine these results. The quotient of the polynomial \( 4x^4 - 8x^3 + 6x^2 \) divided by \( 2x^2 \) is: \[ 2x^2 - 4x + 3 \] Thus, the final answer is \( 2x^2 - 4x + 3 \).