1. Let $f(x)$ be the polynomial \[f(x)=x^7-3x^3+2.\]If $g(x) = f(x + 1)$, what is the sum of the coefficients of $g(x)$?
2. Expand $(2z^2 + 5z - 6)(3z^3 - 2z + 1)$.
+4623 2. Distribute parenthesis, apply minus-plus rules, and solve to get \(6z^5+15z^4-22z^3-8z^2+17z-6\)
+129933 f(x) = x^7 - 3x^3 + 2
g(x) = f(x + 1) = (x + 1)^7 - 3(x+ 1)^3 + 2
The sum of the the coefficients of g(x) =
Sum of the entries in Row 7 of Pascal^s Triangle = 2^7 -
3 * Sum of the entries in Row 3 of Pascal's Triangle = 3*2^3 +
2 =
2^7 - 3*2^3 + 2 = 106
(2z^2 + 5z - 6)(3z^3 - 2z + 1)
2z^2(3z^3 - 2z + 1) + 5z(3z^3 - 2z + 1) - 6(3z^3 - 2z + 1)
6z^5 - 4z^3 + 2z^2 + 15z^4 - 10z^2 + 5z - 18z^3 + 12z - 6 combine like terms
6z^5 + 15z^4 - 22z^3 - 8z^2 + 17z - 6
