Two numbers differ by 12. If their product is increased by the square of their difference, the result is 1008. Find the larger number.

Let the numbers be x and x-12. Then x(x-12) + 144 = 1008, so x²-12x+144 = 1008, giving x²-12x-864 = 0. Solving: x = 36 or x = -24. The two numbers are 36 and 24, but wait — the larger number from (36, 24) is 36; however checking option C (30): if x=30, x-12=18, product=540, square of difference=144, sum=684≠1008. Re-checking with x=36: 36×24=864, 864+144=1008 ✓. The larger number is 36, so correctIndex should be 3.