a/ \(2x+3=0\Rightarrow x=-\frac{3}{2}\)
Để \(P\left(x\right)⋮\left(2x+3\right)\Leftrightarrow P\left(-\frac{3}{2}\right)=0\)
\(\Leftrightarrow m-12=0\Rightarrow m=12\)
\(\Rightarrow P\left(x\right)=6x^3-7x^2-16x+12\)
b/ \(3x-2=0\Rightarrow x=\frac{2}{3}\)
\(P\left(\frac{2}{3}\right)=0\)
\(\Rightarrow P\left(x\right)⋮\left(3x-2\right)\) dư 0 hay \(P\left(x\right)\) chia hết \(3x-2\)
\(6x^3-7x^2-16x+12=\left(2x+3\right)\left(3x-2\right)\left(x-2\right)\)