Đáp án:
$\begin{array}{l}
a)K = {x^4} + 4\\
= {x^4} + 4{x^2} + 4 - 4{x^2}\\
= {\left( {{x^2} + 2} \right)^2} - 4{x^2}\\
= \left( {{x^2} + 2 - 2x} \right)\left( {{x^2} + 2 + 2x} \right)\\
= \left( {{x^2} + 2x + 2} \right)\left( {{x^2} - 2x + 2} \right)\\
b)L = {x^5} + x + 1\\
= {x^5} + {x^4} + {x^3} - {x^4} - {x^3} - {x^2}\\
+ {x^2} + x + 1\\
= {x^3}\left( {{x^2} + x + 1} \right) - {x^2}\left( {{x^2} + x + 1} \right) + \left( {{x^2} + x + 1} \right)\\
= \left( {{x^2} + x + 1} \right)\left( {{x^3} - {x^2} + 1} \right)
\end{array}$
