\(x^3-x^2-14x+24\)

\(=x^3-2x^2+x^2-2x-12x+24\)

\(=x^2\left(x-2\right)+x\left(x-2\right)-12\left(x-2\right)\)

\(=\left(x-2\right)\left(x^2+x-12\right)\)

\(=\left(x-2\right)\left(x^2+4x-3x-12\right)\)

\(=\left(x-2\right)\left[x\left(x+4\right)-3\left(x+4\right)\right]\)

\(=\left(x-2\right)\left(x+4\right)\left(x-3\right)\)

Ta có:\(x^3-x^2-14x+24=\left(x^3-2x^2\right)+\left(x^2-2x\right)-\left(12x-24\right)\)

                                                    \(=x^2\left(x-2\right)+x\left(x-2\right)-12\left(x-2\right)\)

                                                    \(=\left(x-2\right)\left(x^2+x-12\right)\)

                                                    \(=\left(x-2\right)\left(x^2-3x+4x-12\right)\)

                                                    \(=\left(x-2\right)\left[x\left(x-3\right)+4\left(x-3\right)\right]\)

                                                    \(=\left(x-2\right)\left(x+4\right)\left(x-3\right)\)

Ta có:

\(x^3-x^2-14x+24\) \(=x^3+4x^2-5x^2-20x+6x+24\)

                                                    \(=x^2\left(x+4\right)-5x\left(x+4\right)+6\left(x+4\right)\)

                                                    \(=\left(x+4\right)\left(x^2-5x+6\right)\)

                                                    \(=\left(x+4\right)\left(x^2-3x-2x+6\right)\)

                                                    \(=\left(x+4\right)[x\left(x-3\right)-2\left(x-3\right)]\)

                                                    \(=\left(x+4\right)\left(x-2\right)\left(x-3\right).\)

Vậy \(x^3-x^2-14x+24=\left(x+4\right)\left(x-2\right)\left(x-3\right).\)

 x⁴+2.x³-13.x²-14x+24

=x³.(x+2)-13x²+12x-26x+24

=x³.(x+2)-x.(13x-12)-2.(13x-12)

=x³.(x+2)-(13x-12)(x+2)

=(x+2)(x³-13x+12)

=(x+2)(x³-x-12x+12)

=(x+2)[x.(x²-1)-12.(x-1)]

=(x+2)[x.(x-1)(x+1)-12.(x-1)]

=(x+2)(x-1)[x.(x+1)-12]

=(x+2)(x-1)(x²+x-12)

=(x+2)(x-1)(x²-3x+4x-12)

=(x+2)(x-1)[x.(x-3)+4.(x-3)]

=(x+2)(x-1)(x-3)(x+4)

\(b,=x^4-2x^3-x^3+2x^2+3x^2-6x-3x+6\\ =\left(x-2\right)\left(x^3-x^2+3x-3\right)\\ =\left(x-2\right)\left(x-1\right)\left(x^2+3\right)\\ c,=x^4-2x^3+4x^3-8x^2+4x^2-8x+3x-6\\ =\left(x-2\right)\left(x^3+4x^2+4x+3\right)\\ =\left(x-2\right)\left(x^3+3x^2+x^2+3x+x+3\right)\\ =\left(x-2\right)\left(x+3\right)\left(x^2+x+1\right)\)

       \(x^3-9x^2+14x\)

= \(x^3-7x^2-2x^2+14x\)

= \(x^2.\left(x-7\right)-2x.\left(x-7\right)\)

= \(\left(x-7\right).\left(x^2-2x\right)\)

= \(\left(x-7\right).\left(x-2\right).x\)

\(x^3-9x^2+14x\)

\(=x\left(x^2-9x+14\right)\)

\(=x\left(x^2-7x-2x+14\right)\)

\(=x\left[x\left(x-7\right)-2\left(x-7\right)\right]\)

\(=x\left(x-2\right)\left(x-7\right)\)

khó quá tui ko biết làm..

k cho tui nha

thanks

\(x^3-x^2-14x+24\)

\(=x^3+4x^2-5x^2-20x+6x+24\)

\(=\left(x^3+4x^2\right)-\left(5x^2+20x\right)+\left(6x+24\right)\)

\(=x^2\left(x+4\right)-5x\left(x+4\right)+6\left(x+4\right)\)

\(=\left(x^2-5x+6\right)\left(x+4\right)\)

\(=\left(x^2-2x-3x+6\right)\left(x+4\right)\)

\(=\left[x\left(x-2\right)-3\left(x-2\right)\right]\left(x+4\right)\)

\(=\left(x-2\right)\left(x-3\right)\left(x+4\right)\)

\(x^4-14x^3+71x^2-154x+120\)

\(=x^4-2x^3-12x^3+24x^2+47x^2-94x-60x+120\)

\(=x^3\left(x-2\right)-12x^2\left(x-2\right)+47x\left(x-2\right)-60\left(x-2\right)\)

\(=\left(x-2\right)\left(x^3-12x^2+47x-60\right)\)

\(=\left(x-2\right)\left(x^3-3x^2-9x^2+27x+20x-60\right)\)

\(=\left(x-2\right)\left[x^2\left(x-3\right)-9x\left(x-3\right)+20\left(x-3\right)\right]\)

\(=\left(x-2\right)\left(x-3\right)\left(x^2-9x+20\right)\)

\(=\left(x-2\right)\left(x-3\right)\left(x^2-4x-5x+20\right)\)

\(=\left(x-2\right)\left(x-3\right)\left[x\left(x-4\right)-5\left(x-4\right)\right]\)

\(=\left(x-2\right)\left(x-3\right)\left(x-4\right)\left(x-5\right)\)

=x³(x+2)-13x²+12x-26x+24

=x³(x+2)-x(13x-12)-2(13x-12)

=x³(x+2)-(13x-12)(x+2)

=(x+2)(x³-x-12x+12)

(x+2)[(x²-1)-12(x-1)]

=(x+2)[x(x-1)(x+1)-12(x-1)]

=(x+2)(x-1)[x(x+1)-12]

=(x+2)(x-1)(x²+x-12)

=(x+2)(x-1)(x²-3x+4x-12)

=(x+2)(x-1)[x(x-3)+4(x+3)]

=(x+2)(x-1)(x-3)(x+4)

trong bài làm của mk có hàng k có dấu "=" chỗ đó có dâu"=" nha!

   x⁴ + 2x³ - 13x² - 14x + 24
= x⁴ - x³ + 3x³ - 3x² - 10x² + 10x - 24x + 24
= x³(x - 1) + 3x²(x - 1) - 10x(x - 1) - 24(x - 1)
= (x - 1)(x³ + 3x² - 10x - 24)
= (x - 1)(x³ + 2x2 + x² + 2x - 12x - 24)
= (x - 1)[x²(x + 2) + x(x + 2) - 12(x + 2)]
= (x - 1)(x + 2)(x² + x - 12)
= (x - 1)(x + 2)(x² + 4x - 3x - 12)
= (x - 1)(x + 2)[x(x + 4) - 3(x + 4)]
= (x - 1)(x + 2)(x - 3)(x + 4)