Bài 2:
a: \(2x^3+9x^2+15x+9=M\left(2x+3\right)\)
\(\Leftrightarrow M=\dfrac{2x^3+9x^2+15x+9}{2x+3}\)
\(=\dfrac{2x^3+3x^2+6x^2+9x+6x+9}{2x+3}\)
\(=x^2+6x+6\)
b: \(2x^6-x^4-2x^2+1=M\left(2x^2-1\right)\)
\(\Leftrightarrow M=\dfrac{2x^6-x^4-2x^2+1}{2x^2-1}\)
\(=x^4-1\)
Bài II:
a: \(\dfrac{x^4-x^3+6x^2-x+a}{x^2-x+5}\)
\(=\dfrac{x^4-x^3+5x^2+x^2-x+5+a-5}{x^2-x+5}\)
\(=x^2+1+\dfrac{a-5}{x^2-x+5}\)
Để A chia hết cho B thì a-5=0
hay a=5