Đáp án:
b) \(M = {x^3} + 2{x^2} - 5x + 3\)
Giải thích các bước giải:
\(\begin{array}{l}
a)A\left( x \right) = \left( { - 5 + 9} \right){x^3} + \left( { - 2 - 2} \right){x^2} + x - x + 1\\
= 4{x^3} - 4{x^2} + 1\\
B\left( x \right) = \left( { - 4 + 2} \right){x^3} + \left( { - 2 + 2} \right){x^2} + \left( {6 - 9} \right)x - 2\\
= - 2{x^3} - 3x - 2\\
C\left( x \right) = {x^3} - 6{x^2} + 2x - 4\\
b)M\left( x \right) = A\left( x \right) + B\left( x \right) - C\left( x \right)\\
= 4{x^3} - 4{x^2} + 1 - 2{x^3} - 3x - 2 - {x^3} + 6{x^2} - 2x + 4\\
= {x^3} + 2{x^2} - 5x + 3\\
c)P\left( x \right) = 3M\left( x \right) - 3{x^2} - 9 = 0\\
\to 3{x^3} + 6{x^2} - 15x + 9 - 3{x^2} - 9 = 0\\
\to 3{x^3} + 3{x^2} - 15x = 0\\
\to 3x\left( {{x^2} + x - 5} \right) = 0\\
\to \left[ \begin{array}{l}
x = 0\\
x = \dfrac{{ - 1 + \sqrt {21} }}{2}\\
x = \dfrac{{ - 1 - \sqrt {21} }}{2}
\end{array} \right.
\end{array}\)
