The identity 4(z + 7)(2z – 1) = Az2 + Bz + C holds for all real values of z. Find the value of A2 – B – C.

-16 40 36 16

40

4(z + 7)(2z – 1) = Az2 + Bz + C  According to the question, 4(z + 7)(2z – 1)  = 8z2 + 52z - 28 On comparing this expression with Az2 + Bz + C ,  A = 8, B = 52 and C = -28 The value of A2 – B – C = (8)2 - 52 - (-28) = 64 - 52 + 28 = 40