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

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

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

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

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

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

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

      \(x^4+x^3+2x-4\)

\(=x^4-x^3+2x^3-2x^2+2x^2-2x+4x-4\)

\(=x^3\left(x-1\right)+2x^2\left(x-1\right)+2x\left(x-1\right)+4\left(x-1\right)\)

\(=\left(x-1\right)\left(x^3+2x^2+2x+4\right)\)

\(=\left(x-1\right).\left[x^2\left(x+2\right)+2\left(x+2\right)\right]\)

\(=\left(x-1\right)\left(x+2\right)\left(x^2+2\right)\)

      \(8x^4-2x^3-3x^2-2x-1\)

\(=8x^4-8x^3+6x^3-6x^2+3x^2-3x+x-1\)

\(=8x^3\left(x-1\right)+6x^2\left(x-1\right)+3x\left(x-1\right)+x-1\)

\(=\left(x-1\right)\left(8x^3+6x^2+3x+1\right)\)

\(=\left(x-1\right)\left[\left(8x^3+1\right)+\left(6x^2+3x\right)\right]\)

\(=\left(x-1\right)\left[\left(2x+1\right)\left(4x^2-2x+1\right)+3x\left(2x+1\right)\right]\)

\(=\left(x-1\right)\left(2x+1\right)\left(4x^2+x+1\right)\)

      \(3x^2-7x+2\)

\(=3x^2-6x-x+2\)

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

\(=\left(x-2\right)\left(3x-1\right)\)

Chúc bạn học tốt.

mk ghi đáp án, còn lại bạn tự biến đổi

a) \(2x^3-x^2+5x+3=\left(2x+1\right)\left(x^2-x+3\right)\)

b) \(x^3+5x^2+8x+4=\left(x+1\right)\left(x+2\right)^2\)

c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)

d) \(4x^4+1=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)

e) \(x^4-7x^3+14x^2-7x+1=\left(x^2-4x+1\right)\left(x^2-3x+1\right)\)

mk làm chi tiết theo yêu của của người hỏi đề:

a) \(2x^3-x^2+5x+3\)

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

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

\(=\left(2x+1\right)\left(x^2-x+3\right)\)

b)  \(x^3+5x^2+8x+4\)

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

\(=x\left(x^2+4x+4\right)+\left(x^2+4x+4\right)\)

\(=\left(x+1\right)\left(x^2+4x+4\right)\)

\(=\left(x+1\right)\left(x+2\right)^2\)

a) \(x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + x - 1\)
Nhóm các hạng tử:

\(\left(\right. x^{5} - x^{4} \left.\right) + \left(\right. - 2 x^{3} + 2 x^{2} \left.\right) + \left(\right. x - 1 \left.\right) = \left(\right. x - 1 \left.\right) \left(\right. x^{4} - 2 x^{2} + 1 \left.\right) .\)

Đặt \(t = x^{2}\) thì \(x^{4} - 2 x^{2} + 1 = \left(\right. t - 1 \left.\right)^{2} = \left(\right. x^{2} - 1 \left.\right)^{2}\).
Vậy

\(\boxed{x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + x - 1 = \left(\right. x - 1 \left.\right) \left(\right. x^{2} - 1 \left.\right)^{2} = \left(\right. x - 1 \left.\right)^{3} \left(\right. x + 1 \left.\right)^{2} .}\)

b) \(x^{3} - 5 x^{2} - 14 x\)
Lấy \(x\) chung:

\(x \left(\right. x^{2} - 5 x - 14 \left.\right) = x \left(\right. x - 7 \left.\right) \left(\right. x + 2 \left.\right) .\)

\(\boxed{x^{3} - 5 x^{2} - 14 x = x \left(\right. x - 7 \left.\right) \left(\right. x + 2 \left.\right) .}\)

c) \(2 x^{2} + 2 x y - 4 y^{2}\)
Lấy \(2\) chung: \(2 \left(\right. x^{2} + x y - 2 y^{2} \left.\right)\).
Nhân tử hóa: \(x^{2} + x y - 2 y^{2} = \left(\right. x + 2 y \left.\right) \left(\right. x - y \left.\right)\).
\(\boxed{2 x^{2} + 2 x y - 4 y^{2} = 2 \left(\right. x + 2 y \left.\right) \left(\right. x - y \left.\right) .}\)

d) \(3 x^{2} + 8 x y - 3 y^{2}\)
Thử phân tích:

\(3 x^{2} + 8 x y - 3 y^{2} = \left(\right. 3 x - y \left.\right) \left(\right. x + 3 y \left.\right) .\)

\(\boxed{3 x^{2} + 8 x y - 3 y^{2} = \left(\right. 3 x - y \left.\right) \left(\right. x + 3 y \left.\right) .}\)

e) \(x^{2} - x - x y - 2 y^{2} + 2 y\)
Gộp lại theo \(x\): \(x^{2} + x \left(\right. - 1 - y \left.\right) + \left(\right. - 2 y^{2} + 2 y \left.\right)\).
Định thức là một bình phương → nghiệm \(x = 2 y\) và \(x = 1 - y\).
Vậy

\(\boxed{x^{2} - x - x y - 2 y^{2} + 2 y = \left(\right. x - 2 y \left.\right) \left(\right. x + y - 1 \left.\right) .}\)

f) \(x^{2} + 2 y^{2} - 3 x y + x - 2 y\)
Xem như phương trình bậc hai theo \(x\): nghiệm \(x = 2 y\) và \(x = y - 1\).
Do đó

\(\boxed{x^{2} + 2 y^{2} - 3 x y + x - 2 y = \left(\right. x - 2 y \left.\right) \left(\right. x - y + 1 \left.\right) .}\)

a: \(x^5-x^4-2x^3+2x^2+x-1\)

\(=x^4\left(x-1\right)-2x^2\left(x-1\right)+\left(x-1\right)\)

\(=\left(x-1\right)\left(x^4-2x^2+1\right)\)

\(=\left(x-1\right)\left(x^2-1\right)^2=\left(x-1\right)\cdot\left(x-1\right)^2\cdot\left(x+1\right)^2\)

\(=\left(x-1\right)^3\cdot\left(x+1\right)^2\)

b: \(x^3-5x^2-14x\)

\(=x\left(x^2-5x-14\right)\)

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

=x[x(x-7)+2(x-7)]

=x(x-7)(x+2)

c: \(2x^2+2xy-4y^2\)

\(=2\left(x^2+xy-2y^2\right)\)

\(=2\left(x^2+2xy-xy-2y^2\right)\)

=2[x(x+2y)-y(x+2y)]

=2(x+2y)(x-y)

d: \(3x^2+8xy-3y^2\)

\(=3x^2+9xy-xy-3y^2\)

=3x(x+3y)-y(x+3y)

=(x+3y)(3x-y)

e: \(x^2-x-xy-2y^2+2y\)

\(=\left(x^2-xy-2y^2\right)-\left(x-2y\right)\)

\(=\left(x^2-2xy+xy-2y^2\right)-\left(x-2y\right)\)

=x(x-2y)+y(x-2y)-(x-2y)

=(x-2y)(x+y-1)

f: \(x^2+2y^2-3xy+x-2y\)

\(=x^2-2xy-xy+2y^2+x-2y\)

=x(x-2y)-y(x-2y)+(x-2y)

=(x-2y)(x-y+1)

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

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

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

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

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

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

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

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

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

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

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

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

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

\(x^3-5x^2-14x\)

\(=x^3+2x^2-7x^2-14x\)

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

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

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

\(x^3-7x-6\)

\(=x^3+x^2-x^2-x-6x-6\)

\(=x^2\left(x+1\right)-x\left(x+1\right)-6\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-x-6\right)\)

\(=\left(x+1\right)\left(x^2+2x-3x-6\right)\)

\(=\left(x+1\right)\left[x\left(x+2\right)-3\left(x+2\right)\right]\)

\(=\left(x+1\right)\left(x+2\right)\left(x-3\right)\)

\(x^3-19x-30\)

\(=x^3-5x^2+5x^2-25x+6x-30\)

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

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

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

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

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

\(g,x^2-2xy+y^2-9z^2=\left(x-y\right)^2-\left(3z\right)^2\)\(=\left(x-y+3z\right)\left(x-y-3z\right)\)

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

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

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

\(k,x^2+8x+3x+24=x\left(x+8\right)+3\left(x+8\right)=\left(x+8\right)\left(x+3\right)\)

\(m,x^4-y^4=\left(x^2-y^2\right)\left(x^2+y^2\right)=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\)

\(n,x^6-y^6=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)=\left(x-y\right)\left(x+y\right)\left(x^4+x^2y^2+y^4\right)\)

a) \(x^3-7x-6=x^3-x^2+x^2-7x-6=x^2\left(x-1\right)+x^2-x-6x+6\)

\(=x^2\left(x-1\right)+\left(x\left(x-1\right)-6\left(x-1\right)\right)\)

\(=\left(x-1\right)\left(x^2+x-6\right)=\left(x-1\right)\left(x^2-2x+3x-6\right)\)

\(\left(x-1\right)\left(x\left(x-2\right)+3\left(x-2\right)\right)=\left(x-1\right)\left(x-2\right)\left(x+3\right)\)

b)\(x^3-x^2-14x+24=x^3-3x^2+2x^2-6x-8x+24\)

\(=x^2\left(x-3\right)+2x\left(x-3\right)-8\left(x-3\right)\)

\(=\left(x-3\right)\left(x^2+2x-8\right)=\left(x-3\right)\left(x^2-2x+4x-8\right)\)

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

  CÓ CHỖ NÀO KO HIỂU GỬI THƯ HỎI MIK , MIK NÓI CHO !!~  HOK TỐT ~

a, \(x^4+6x^3+7x^2-6x+1\)

\(=x^4-2x^2+1+6x^3+9x^2+6x\)

\(=\left(x^2-1\right)^2+6x\left(x^2-1\right)+9x^2\)

\(=\left(x^2-1+3x\right)^2\)

b, \(x^4-7x^3+14x^2-7x+1\)

\(=x^4+2x^2+1+7x^3+12x^2-7x\)

\(=\left(x^2+1\right)^2-7x\left(x^2+1\right)+12^2\)

\(=\left(x^2-1+3x\right)^2\)

c, \(12x^2-11x-36\)

\(=12x^2-27x+16x-36\)

\(=3x\left(4x-9\right)+4\left(4x-9\right)\)

\(=\left(4x-9\right)\left(3x+4\right)\)