1. **State the problem:** We need to find which expression (A, B, or C) is equivalent to each given subtraction of polynomials. 2. **Recall the formula:** When subtracting polynomials, subtract each corresponding term: $$ (P) - (Q) = (a_1x^2 + b_1x + c_1) - (a_2x^2 + b_2x + c_2) = (a_1 - a_2)x^2 + (b_1 - b_2)x + (c_1 - c_2) $$ 3. **Calculate each expression:** - For $ (3x^2 - 6x + 11) - (10x^2 - 4x + 6) $: $$ 3x^2 - 6x + 11 - 10x^2 + 4x - 6 = (3 - 10)x^2 + (-6 + 4)x + (11 - 6) = -7x^2 - 2x + 5 $$ This matches expression A. - For $ (-3x^2 - 5x - 3) - (-10x^2 - 7x + 2) $: $$ -3x^2 - 5x - 3 + 10x^2 + 7x - 2 = (-3 + 10)x^2 + (-5 + 7)x + (-3 - 2) = 7x^2 + 2x - 5 $$ This matches expression C. - For $ (12x^2 + 6x - 5) - (5x^2 + 8x - 12) $: $$ 12x^2 + 6x - 5 - 5x^2 - 8x + 12 = (12 - 5)x^2 + (6 - 8)x + (-5 + 12) = 7x^2 - 2x + 7 $$ This matches expression B. 4. **Final answers:** - First expression equivalent to A - Second expression equivalent to C - Third expression equivalent to B