If the coefficient of $x$ in the expansion of $(ax^2+bx+c)(1-2x)^{26}$ is $-56$ and the coefficients of $x^2$ and $x^3$ are both zero, then $a+b+c$ is equal to:
Step-by-Step Solution
Key Concept: In $(1-2x)^{26}$: $T_0=1$, $T_1=-52x$, $T_2=1300x^2$, $T_3=-20800x^3$. Set up equations from coeff of $x=-56$, coeff of $x^2=0$, coeff of $x^3=0$.
$c=3,b=100,a=1300$. $a+b+c=1403$.
Correct Answer: 3