Expand out the right bit.
(Ax+1)^2+B(x-2)+C = A2x2+2Ax + 1 + Bx - 2B + C
= (A2)x2 + (2A + B)x + (1 - 2B + C) (collect like terms)
Equate coefficients of terms x2, x and the constants with the equation, ie. 9x2 + 4x + 16
So A2= 9, (2A + B) = 4, (1 - 2B + C) = 16
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A = 3...