Đáp án:
$\begin{array}{l}
a)a + b + c = 0\\
\Leftrightarrow a = - b - c\\
A = {b^3} + {c^3} + a{b^2} + a{c^2} - abc\\
= {b^3} + {c^3} + \left( { - b - c} \right).{b^2} + \left( { - b - c} \right).{c^2}\\
- \left( { - b - c} \right).bc\\
= {b^3} + {c^3} - {b^3} - {b^2}c - b{c^2} - {c^3}\\
+ {b^2}c + b{c^2}\\
= 0\\
b)B = {x^5} - 5{x^4} + 5{x^3} - 5{x^2} + 5x - 1\\
= {x^5} - 4{x^4} - {x^4} + 4{x^3}\\
+ {x^3} - 4{x^2} - {x^2} + 4x + x - 4 + 3\\
= {x^4}\left( {x - 4} \right) - {x^3}\left( {x - 4} \right)\\
+ {x^2}\left( {x - 4} \right) - x\left( {x - 4} \right) + \left( {x - 4} \right) + 3\\
= \left( {x - 4} \right)\left( {{x^4} - {x^3} + {x^2} - x + 1} \right) + 3\\
= \left( {4 - 4} \right).\left( {{4^4} - {4^3} + {4^2} - 4 + 1} \right) + 3\\
= 3\\
c)C = {x^7} - 80{x^6} + 80{x^5} - 80{x^4} + ... + 80x + 15\\
= {x^7} - 79{x^6} - {x^6} + 79{x^5} + {x^5} - 79{x^4} - ...\\
- {x^2} + 79x + x - 79 + 94\\
= \left( {x - 79} \right)\left( {{x^6} - {x^5} + {x^4} - {x^3} + {x^2} - x + 1} \right) + 94\\
= 94\left( {khi:x = 79} \right)
\end{array}$
