phân tích
2x2+5x+2
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\(\left(x^2+5x\right)^2-2\left(x^2+5x\right)-24\\ =\left[\left(x^2+5x\right)^2-6\left(x^2+5x\right)\right]+\left[4\left(x^2+5x\right)-24\right]\\ =\left(x^2+5x\right)\left(x^2+5x-6\right)+4\left(x^2+5x-6\right)\\ =\left(x^2+5x-6\right)\left(x^2+5x+4\right)\\ =\left(x^2-x+6x-6\right)\left(x^2+4x+x+4\right)\\ =\left[x\left(x-1\right)+6\left(x-1\right)\right]+\left[x\left(x+4\right)+\left(x+4\right)\right]\\ =\left(x-1\right)\left(x+1\right)\left(x+4\right)\left(x+6\right)\)
\(x^2+5x-6\\ =x^2-x+6x-6\\ =x\left(x-1\right)+6\left(x-1\right)\\ =\left(x+6\right)\left(x-1\right)\\ ---\\ 5x^2+5xy-x-y\\ =x\left(5x-1\right)+y\left(5x-1\right)\\ =\left(5x-1\right)\left(x+y\right)\\ ----\\ 7x-6x^2-2\\ =-6x^2+3x+4x-2\\ =-3x\left(2x-1\right)+2\left(2x-1\right)\\ =\left(2-3x\right)\left(2x-1\right)\)
\(x^2+5x-6=\left(x-1\right)\left(x+6\right)\\ 5x^2+5xy-x-y=\left(5x-1\right)\left(x+y\right)\\ 7x-6x^2-2=\left(3x-2\right)\left(2x-1\right)\)
\(5x^2-5x-10=5x^2+5x-10x-10=5x\left(x+1\right)-10\left(x+1\right)=\left(5x-10\right)\left(x+1\right)\)
5x2−5x−10=5x2+5x−10x−10=5x(x+1)−10(x+1)=(5x−10)(x+1)
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\(2x^2+5x+2\)
\(=2x^2+4x+x+2\)
\(=2x\left(x+2\right)+x+2\)
\(=\left(x+2\right)\left(2x+1\right)\)
2x2 + 5x + 2
= 2x2 + 4x + x + 2
= (2x2 + 4x) + (x + 2)
= 2x (x + 2) + (x + 2)
= (2x + 1) (x + 2)