Find the sum of the coefficients in the polynomial $3(3x^{7} + 8x^4 - 7) + 7(x^5 - 7x^2 + 5)$ when it is fully simplified.
3(3x7 + 8x4 - 7) + 7(x5 - 7x2 + 5)
= 9x7 + 24x4 - 21 + 7x5 - 49x2 + 35
= 9x7 + 7x5 + 24x4 - 49x2 + 14
The sum of the coefficients = 9 + 7 + 24 - 49 = -9, which is your answer :)