1. **State the problem:** We need to subtract the polynomial $ (5k^2 - 3) $ from $ (-2k + 4k^2 + 6) $. 2. **Write the expression:** $$ (-2k + 4k^2 + 6) - (5k^2 - 3) $$ 3. **Distribute the minus sign to the second polynomial:** $$ -2k + 4k^2 + 6 - 5k^2 + 3 $$ 4. **Combine like terms:** - For the $ k^2 $ terms: $4k^2 - 5k^2 = \cancel{4k^2} - \cancel{5k^2} = -1k^2 = -k^2$ - For the $ k $ terms: $-2k$ (no like term to combine) - For the constants: $6 + 3 = 9$ 5. **Write the final polynomial in standard form (descending powers):** $$ -k^2 - 2k + 9 $$ **Answer:** $ -k^2 - 2k + 9 $