Bài 1:
\(x^2-y^2-2y-1=x^2-\left(y^2+2y+1\right)=x^2-\left(y+1\right)^2=\left(x-y-1\right)\left(x+y+1\right)\)
Bài 2:
\(2\left(x+3\right)-x^2-3x=0\)
\(\Rightarrow2\left(x+3\right)-x\left(x+3\right)=0\Rightarrow\left(x+3\right)\left(2-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-3\\x=2\end{matrix}\right.\)
Bài 3:
\(A=4x-x^2=-\left(x^2-4x+4\right)+4=-\left(x-2\right)^2+4\le4\)
\(maxA=4\Leftrightarrow x=2\)
Bài 4:
\(A\left(x\right)=2x^3-7x^2+5x+m=x^2\left(2x-3\right)-2x\left(2x-3\right)-x+m\)
\(=\left(2x-3\right)\left(x^2-2x\right)-x+m⋮B\left(x\right)=2x-3\)
\(\Rightarrow-x+m=0\Rightarrow m=x\)
Bài 5:
\(x+y=3\Rightarrow\left(x+y\right)^2=9\Rightarrow x^2+y^2=9-2xy=9-2.2=5\)
\(x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)=3\left(5-2\right)=9\)
