a) \(x^2+7x+12\)
\(=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x+3\right)\left(x+4\right)\)
c) \(x^2+8x-9\)
\(=x^2-x+9x-9\)
\(=x\left(x-1\right)+9\left(x-1\right)\)
\(=\left(x-1\right)\left(x+9\right)\)
d) \(x^4+5x^2-6\)
\(=x^4-x^2+6x^2-6\)
\(=x^2\left(x^2-1\right)+x\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+x\right)\)
\(=x\left(x-1\right)\left(x+1\right)\left(x+1\right)\)
\(=x\left(x-1\right)\left(x+1\right)^2\)
\(\text{a) }x^2+7x+12\\ =x^2+3x+4x+12\\ =\left(x^2+3x\right)+\left(4x+12\right)\\ =x\left(x+3\right)+4\left(x+3\right)\\ =\left(x+4\right)\left(x+3\right)\\ \)
\(\text{b) }3x^2+7x-6\\ =3x^2+9x-2x-6\\ =\left(3x^2+9x\right)-\left(2x+6\right)\\ =3x\left(x+3\right)-2\left(x+3\right)\\ =\left(3x+2\right)\left(x+3\right)\\ \)
\(\text{c) }x^2+8x-9\\ =x^2+9x-x-9\\ =\left(x^2+9x\right)-\left(x+9\right)\\ =x\left(x+9\right)-\left(x+9\right)\\ =\left(x-1\right)\left(x+9\right)\\ \)
\(\text{d) }x^4+5x^2-6\\ =x^4+2x^2+3x^2-6\\ =x^4+6x^2-x^2-6\\ =\left(x^4+6x^2\right)-\left(x^2+6\right)\\ =x^2\left(x^2+6\right)-\left(x^2+6\right)\\ =\left(x^2-1\right)\left(x^2+6\right)\\ =\left(x-1\right)\left(x+1\right)\left(x^2+6\right)\\ \)
Mk nhầm một số chỗ ở câu d. Cho phép làm lại:
\(\text{d) }x^4+5x^2-6\\ =x^4+6x^2-x^2-6\\ =\left(x^4+6x^2\right)-\left(x^2+6\right)\\ =x^2\left(x^2+6\right)-\left(x^2+6\right)\\ =\left(x^2-1\right)\left(x^2+6\right)\\ =\left(x-1\right)\left(x+1\right)\left(x^2+6\right)\)
