Đáp án:
\(m=27\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\,\,A\left( x \right) = 2{x^2} - 4{x^2} + mx + 3m - 19\\
\,\,\,\,\,\,A\left( x \right) = - 2{x^2} + mx + 3m - 19\\
\,\,\,\,\,\,B\left( x \right) = x + 2\\
Thay\,\,m = 30\\
\Rightarrow A\left( x \right) = - 2{x^2} + 30x + 3.30 - 19\\
\,\,\,\,\,\,A\left( x \right) = - 2{x^2} + 30x + 71\\
\,\,\,\,\,\,B\left( x \right) = x + 2\\
b)\,A\left( x \right) = - 2{x^2} + mx + 3m - 19\\
\,\,\,\,\,A\left( x \right) = - 2{x^2} - 4x + \left( {m + 4} \right)x + 2\left( {m + 4} \right) + m - 27\\
\,\,\,\,\,A\left( x \right) = - 2x\left( {x + 2} \right) + \left( {m + 4} \right)\left( {x + 2} \right) + m - 27\\
\,\,\,\,\,\,A\left( x \right) = \left( {x + 2} \right)\left( { - 2x + m + 4} \right) + m - 27\\
A\left( x \right)\,\, \vdots \,\,B\left( x \right) \Leftrightarrow m - 27 = 0 \Leftrightarrow m = 27
\end{array}\)
