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\(2x^2+5x+3=2x^2+2x+3x+3=2x\left(x+1\right)+3\left(x+1\right)=\left(2x+3\right)\left(x+1\right)\)
\(2x^2+5x+3=2x^2+2x+3x+3=\left(2x^2+2x\right)+\left(3x+3\right)=2x\left(x+1\right)+3\left(x+1\right)=\left(x+1\right)\left(2x+3\right)\)
\(2x^2+5x-3\\ =2x^2+6x-x-3\\ =2x\left(x+3\right)-\left(x+3\right)\\ =\left(x+3\right)\left(2x-1\right)\)
x 4 - 2 x 3 - 2 x 2 - 2 x - 3 = ( x 4 − 1 ) − ( 2 x 3 + 2 x 2 ) − ( 2 x + 2 ) = ( x 2 + 1 ) ( x 2 − 1 ) − 2 x 2 ( x + 1 ) − 2 ( x + 1 ) = ( x 2 + 1 ) ( x − 1 ) ( x + 1 ) − 2 x 2 ( x + 1 ) − 2 ( x + 1 ) = ( x + 1 ) ( x 2 + 1 ) ( x − 1 ) − 2 x 2 – 2 = ( x + 1 ) ( x 2 + 1 ) ( x − 1 ) − 2 ( x 2 + 1 ) = ( x + 1 ) ( x 2 + 1 ) ( x – 1 − 2 ) = ( x + 1 ) ( x 2 + 1 ) ( x − 3 )
x^4 - 2x^3 - 2x^2 - 2x - 3
= x^4 - 1 - 2x^3 - 2x^2 - 2x -2
= ( x - 1 ) ( x + 1 ) ( x^2 + 1 ) - 2x^2 ( x + 1 ) - 2 ( x + 1 )
= ( x + 1 ) [ ( x - 1 ) ( x^2 + 1 ) - 2x^2 - 2 ]
= ( x + 1 ) [ ( x - 1 ) ( x^2 + 1 - 2 ( x^2 - 1 ) ]
= ( x + 1 ) [ ( x - 1 ) ( x^2 + 1 ) - 2 ( x - 1 ) ( x + 1 ) ]
= ( x + 1 ) ( x - 1 ) [ ( x^2 + 1 ) - 2 ( x +1 )
= ( x + 1 ) ( x - 1 ) ( x^2 +1 - 2x - 2 )
= ( x + 1 ) ( x - 1 ) ( x^2 - 2x - 1 )
\(=\left(2x^2+xy-3x\right)-\left(22xy+11y^2-33y\right)+\left(2x+y-3\right)\)
\(=x\left(2x+y-3\right)-11y\left(2x+y-3\right)+\left(2x+y-3\right)\)
\(=\left(x-11y+1\right)\left(2x+y-3\right)\)
\(2x^2+xy-y^2=\left(x^2-xy\right)+\left(x^2-y^2\right)=x\left(x-y\right)+\left(x-y\right)\left(x+y\right)=\left(x-y\right)\left[x+\left(x-y\right)\right]=\left(x-y\right)\left(x+x-y\right)=\left(x-y\right)\left(2x+y\right)\)
1: \(-x^2+2x+8\)
\(=-\left(x^2-2x-8\right)\)
\(=-\left(x-4\right)\left(x+2\right)\)
2: \(2x^2-3x+1=\left(x-1\right)\left(2x-1\right)\)
a) 2x2- 6x2
= -4x2
b) x2-6x+9-y2
= (x-3)2 -y2
= (x-3-y).(x-3+y)
\(=-2\left(x^2-2xy+y^2-4\right)\)
\(=-2\left[\left(x-y\right)^2-4\right]\)
\(=-2\left(x-y-2\right)\left(x-y+2\right)\)
\(2x^2-7+3=2x^2-6x-x+3=2x\left(x-3\right)-\left(x-3\right)=\left(x-3\right)\left(2x-1\right)\)
\(2x^2-7+3\\ =2x^2-4\\ =2\left(x^2+2\right).\)