Bài 5:
1) \(x^2+2x-8\)
\(=x^2+4x-2x-8\)
\(=x\left(x+4\right)-2\left(x+4\right)\)
\(=\left(x+4\right)\left(x-2\right)\)
2) \(x^2+5x+6\)
\(=x^2+3x+2x+6\)
\(=x\left(x+3\right)+2\left(x+3\right)\)
\(=\left(x+2\right)\left(x+3\right)\)
3) \(4x^2-12x+8\)
\(=4\left(x^2-3x+2\right)\)
\(=4\left(x^2-x-2x+2\right)\)
\(=4\left[x\left(x-1\right)-2\left(x-1\right)\right]\)
\(=4\left(x-1\right)\left(x-2\right)\)
4) \(x^2+6x+8\)
\(=x^2+2x+4x+8\)
\(=x\left(x+2\right)+4\left(x+2\right)\)
\(=\left(x+2\right)\left(x+4\right)\)
5) \(x^2+10x+16\)
\(=x^2+8x+2x+16\)
\(=x\left(x+8\right)+2\left(x+8\right)\)
\(=\left(x+2\right)\left(x+8\right)\)
6) \(\left(x+1\right)^2-4\)
\(=\left[\left(x+1\right)-2\right]\left[\left(x+1\right)+2\right]\)
\(=\left(x+1-2\right)\left(x+1+2\right)\)
\(=\left(x-1\right)\left(x+3\right)\)
7) \(9-6x+x^2-y^2\)
\(=\left(9-6x+x^2\right)-y^2\)
\(=\left(3-x\right)^2-y^2\)
\(=\left(3-x-y\right)\left(3-x+y\right)\)
8) \(x^2+3x+2\)
\(=x^2+2x+x+2\)
\(=x\left(x+2\right)+\left(x+2\right)\)
\(=\left(x+2\right)\left(x+1\right)\)
9) \(x^2-x-2\)
\(=x^2+x-2x-2\)
\(=x\left(x+1\right)-2\left(x+1\right)\)
\(=\left(x+1\right)\left(x-2\right)\)
10) \(x^2-x-6\)
\(=x^2+2x-3x-6\)
\(=x\left(x+2\right)-3\left(x+2\right)\)
\(=\left(x+2\right)\left(x-3\right)\)
4:
1: =x(x^3-9x^2+x-9)
=x[x^2(x-9)+(x-9)]
=x(x-9)(x^2+1)
2: =3x(x-y)-5(x-y)
=(x-y)(3x-5)
3: =y(x+1)+z(x+1)
=(x+1)(y+z)
4: =x(x-y)-(x-y)
=(x-y)(x-1)
