\[\boxed{\mathbf{299}.}\]
\[\left( x^{3} + ax + 1 \right)\ :(x - a)\]
\[x^{3} + ax + 1 =\]
\[= (x - a) \cdot M(x) + 3\]
\[1\] | \[0\] | \[a\] | \[1\] | |
---|---|---|---|---|
\[a\] | \[1\] | \[a\] | \[a + a^{2}\] | \[1 + a^{2} + a^{3}\] |
\[a^{3} + a^{2} + 1 = 3\]
\[a^{3} + a^{2} - 2 = 0\]
\[a = 1.\]
\[Ответ:a = 1.\text{\ \ }\]