Đáp án:
\[a = - 50\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
f\left( x \right) = 18{x^2} + a\\
= \left( {18{x^2} + 30x} \right) + \left( { - 30x - 50} \right) + \left( {a + 50} \right)\\
= 6x.\left( {3x + 5} \right) - 10.\left( {3x + 5} \right) + \left( {a + 50} \right)\\
= \left( {3x + 5} \right)\left( {6x - 10} \right) + \left( {a + 50} \right)\\
f\left( x \right)\,\, \vdots \,\,\left( {3x + 5} \right)\\
\Leftrightarrow \left[ {\left( {3x + 5} \right)\left( {6x - 10} \right) + \left( {a + 50} \right)} \right]\,\, \vdots \,\,\left( {3x + 5} \right)\\
\left( {3x + 5} \right)\left( {6x - 10} \right)\,\, \vdots \,\,\left( {3x + 5} \right)\\
\Rightarrow \left( {a + 50} \right)\,\, \vdots \,\,\left( {3x + 5} \right),\,\,\,\forall x\\
\Rightarrow a + 50 = 0\\
\Leftrightarrow a = - 50
\end{array}\)
Vậy \(a = - 50\)
