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\(x^3-3x^2-4x+12\)
\(=x^2\left(x-3\right)-\left(4x-12\right)\)
\(=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x^2-4\right)\left(x-3\right)\)
\(=\left(x+2\right)\left(x-2\right)\left(x-3\right)\)
\(x^3-3x^2-4x+12\)
\(=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x^2-4\right)\left(x-3\right)\)
\(=\left(x+2\right)\left(x-2\right)\left(x-3\right)\)
\(\left(x^2-2x\right)\left(x^2-2x-2\right)-6=x^4-2x^3-x^2-2x^3+4x^2+2x-6\)
\(=x^4-4x^3+3x^2+2x-6\)
\(=\left(x^4+x^3\right)-\left(5x^3+5x^2\right)+\left(8x^2+8x\right)-\left(6x+6\right)\)
\(=x^3\left(x+1\right)-5x^2\left(x+1\right)+8x\left(x+1\right)-6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3-5x^2+8x-6\right)=\left(x+1\right)\left(x-3\right)\left(x^2-2x+2\right)\)
\(x^3+2x^2+x\)
\(=x\left(x^2+2x+1\right)\)
\(=x\left(x+1\right)^2\)
\(=\left(x^2+4x-3\right)^2-5\left(x^2+4x-3\right)+6x^2\)
\(=x^4+16x^2+9+8x^3-24x-6x^2-5x^2-20x+15+6x^2\)
\(=x^4+8x^3+11x^2-44x+24\)
\(=\left(x^4-x^3\right)+\left(9x^3-9x^2\right)+\left(20x^2-20x\right)-\left(24x-24\right)\)
\(=x^3\left(x-1\right)+9x^2\left(x-1\right)+20x\left(x-1\right)-24\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+9x^2+20x-24\right)\)
\(1)x^3-x^2y-4x-4y=x^2\left(x-y\right)-4\left(x-y\right)=\left(x^2-2^2\right)\left(x-y\right)=\left(x^2-4x+4\right)\left(x-y\right)\)
\(2)x^3-3x^2+1-3x=\left(x^3+1\right)-3x\left(x-1\right)=\left(x+1\right)\left(x^2-x+1\right)-3x\left(x-1\right)\)
\(25-9y^2\)
\(=5^2-\left(3y\right)^2\)
\(=\left(5-3y\right)\left(5+3y\right)\)
\(4\left(x+3y-4\right)^2-x^2+6x-9\)
\(=\left[2\left(x+3y-4\right)\right]^2-\left(x^2-6x+9\right)\)
\(=\left[2x+6y-8\right]^2-\left(x-3\right)^2\)
\(=\left(2x+6y-8+x-3\right)\left(2x+6y-8-x+3\right)\)
\(=\left(3x+6y-11\right)\left(x+6y-5\right)\)
x^2 -x - 2x + 2
= x ( x - 1 ) -2 ( x - 1)
=( x - 2 ) . (x -1)
tick nha