Substitute x = -1 into the function f(x).

Here are the solutions to the problems:

29. Given that $f(x) = 2x^3 + 5x^2 + mx - 7$, the value of $m$ for which $f(-1) = 0$ is:

Step 1: Substitute $x = -1$ into the function $f(x)$.

$$f(-1) = 2(-1)^3 + 5(-1)^2 + m(-1) - 7$$

Step 2: Simplify the expression.

$$f(-1) = 2(-1) + 5(1) - m - 7$$ $$f(-1) = -2 + 5 - m - 7$$ $$$$