somebody help me 

\(1,2x^2-3x-2\) 

\(=2x^2-4x+x-2\)

\(=2x\left(x-2\right)+\left(x-2\right)\) 

\(=\left(2x+1\right)\left(x-2\right)\) 

\(2,4x^2-7x-2\)

\(=4x^2-8x+x-2\) 

\(=4x\left(x-2\right)+x-2\)

\(\left(4x+1\right)\left(x-2\right)\)

\(8x^2+4x+4=4\left(2x^2+x+1\right)\)

\(\left(2x-y\right)\left(4x^2-4xy+y^2\right)-8x^2\left(x-y\right)\)

\(=\left(2x-y\right)^3-8x^2\left(x-y\right)\)

\(=8x^3-12x^2y+6xy^2-y^3-8x^3+8x^2y\)

\(=-4x^2y-6xy^2-y^3\)

\(=-y\left(4x^2+6xy+y^2\right)\)

\(x^3+5x^2+5x+1\)

\(=\left(x+1\right)\left(x^2+x+1\right)+5x\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2+6x+1\right)\)

#)Giải :

\(x^3-2x-4\)

\(=x^3+2x^2-2x^2+2x-4x-4\)

\(=x^3+2x^2+2x-2x^2-4x-4\)

\(=x\left(x^2+2x+2\right)-2\left(x^2+2x+2\right)\)

\(=\left(x-2\right)\left(x^2+2x+2\right)\)

\(x^4+2x^3+5x^2+4x-12\)

\(=x^4+x^3+6x^2+x^3+x^2+6x-2x^2-2x-12\)

\(=x^2\left(x^2+x+6\right)+x\left(x^2+x+6\right)-2\left(x^2+x+6\right)\)

\(=\left(x^2+x+6\right)\left(x^2+x-2\right)\)

\(=\left(x^2+x+6\right)\left(x-1\right)\left(x+2\right)\)

Câu 1.

Đoán được nghiệm là 2.Ta giải như sau:

\(x^3-2x-4\)

\(=x^3-2x^2+2x^2-4x+2x-4\)

\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)

\(=\left(x-2\right)\left(x^2+2x+2\right)\)

\(2x^2+5x+3=2x^2+2x+3x+3=2x\left(x+1\right)+3\left(x+1\right)=\left(2x+3\right)\left(x+1\right)\)

\(2x^2+5x+3=2x^2+2x+3x+3=\left(2x^2+2x\right)+\left(3x+3\right)=2x\left(x+1\right)+3\left(x+1\right)=\left(x+1\right)\left(2x+3\right)\)

\(2x^2+5x-3\\ =2x^2+6x-x-3\\ =2x\left(x+3\right)-\left(x+3\right)\\ =\left(x+3\right)\left(2x-1\right)\)

\(=2x^2-6x+x-3=\left(x-3\right)\left(2x+1\right)\)

\(=2x^2-6x+x-3=2x\left(x-3\right)+\left(x-3\right)=\left(2x+1\right)\left(x-3\right)\)

\(16x-5x^2-3=-\left(5x^2-16x+3\right)=-\left[\left(5x^2-15x\right)-\left(x-3\right)\right]=-\left[5x\left(x-3\right)-\left(x-3\right)\right]=-\left(5x-1\right)\left(x-3\right)=\left(5x-1\right)\left(3-x\right)\)