a) \(x^3-5x^2+8x-4\)
= \(x^3-x^2-4x^2+4x+4x-4\)
= \(x^2\left(x-1\right)-4x\left(x-1\right)+4\left(x-1\right)\)
= \(\left(x-1\right)\left(x^2-4x+4\right)\)
= \(\left(x-1\right)\left(x-2\right)^2\)
b) \(x^3-9x^2+6x+16\)
= \(\left(x-8\right)\left(x-2\right)\left(x+1\right)\)
c) \(x^3+2x-3\)
= \(x^3-x^2+x^2-x+3x-3\)
= \(x^2\left(x-1\right)+x\left(x-1\right)+3\left(x-1\right)\)
= \(\left(x-1\right)\left(x^2+x+3\right)\)
d) \(2x^3-12x^2+17x-2\)
= \(2x^3-4x^2-8x^2+16x+x-2\)
= \(2x^2\left(x-2\right)-8x\left(x-2\right)+\left(x-2\right)\)
= \(\left(x-2\right)\left(2x^2-8x+1\right)\)
e) \(x^3-5x^2+3x+9\)
= \(x^3+x^2-6x^2-6x+9x+9\)
= \(x^2\left(x+1\right)-6x\left(x+1\right)+9\left(x+1\right)\)
= \(\left(x+1\right)\left(x^2-6x+9\right)=\left(x+1\right)\left(x-3\right)^2\)
f) \(x^3-8x^2+17x+10\)
Câu này có vẻ sai đề, nghiệm cực kì khủng bố @@
g) \(x^3-2x-4\)
= \(x^3-2x^2+2x^2-4x+2x-4\)
= \(x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
= \(\left(x-2\right)\left(x^2+2x+2\right)\)
h) \(x^3+x^2+4\)
= \(x^3+2x^2-x^2+4\)
= \(x^2\left(x+2\right)-\left(x-2\right)\left(x+2\right)\)
= \(\left(x+2\right)\left(x^2-x+2\right)\)
i) \(x^3-7x+6\)
= \(\left(x+3\right)\left(x-2\right)\left(x-1\right)\)
