If 4(z + 7) (2z – 1) = Az² + Bz + C, then the value of A + B + C is:

Correct option is B

Given:

We are given the equation 4(z + 7)(2z - 1) and need to find A + B + C after expanding and comparing it to Az² + Bz + C.

Formula Used:

We will expand the expression using the distributive property and collect the terms for z², z, and the constant.

Solution:

First, expand the expression 4(z + 7)(2z - 1):

4(z + 7)(2z - 1) = 4z(2z - 1) + 7(2z - 1)

= 4(2z² - z + 14z – 7)

= 4(2z² + 13z – 7)

= 8z² + 52z - 28

By comparing with the expression Az² + Bz + C, we have:

A = 8, B = 52, C = -28

Therefore, A + B + C:

A + B + C = 8 + 52 - 28

= 32

Therefore, the value of A + B + C is 32.