If A = -2x² + 12x, B = 11 - 8x + 3x², C = 17 - 4x² and D = x² - x - 3, then…

When two or more polynomials are combined by addition or subtraction, the coefficients of each power of x combine independently — the x2 terms combine among themselves, the x terms combine among themselves, and the constant terms combine among themselves. To find the sum of two different-degree coefficients in a combination such as A + B + C − D, first work out each coefficient (of x2 and of x) separately from the combination, then add the two resulting numbers.

Here A = -2x2 + 12x, B = 3x2 - 8x + 11, C = -4x2 + 17 and D = x2 - x - 3.

1. Coefficient of x2: taking it from A, B, C and -D in turn, -2 + 3 + (-4) - 1 = -4.

2. Coefficient of x: taking it from A, B, C and -D in turn, 12 + (-8) + 0 - (-1) = 12 - 8 + 1 = 5.

3. Sum of the two coefficients: -4 + 5 = 1.

As an independent check, expand the full combination directly: A + B + C - D = (-2+3-4-1)x2 + (12-8+0+1)x + (0+11+17+3) = -4x2 + 5x + 31. Reading off the x2 and x coefficients from this expanded form gives the same values, -4 and 5, confirming the result.

So the required sum of the coefficients of x2 and x is 1.