\(3x^4+6x^3-7x^2+8x-10\)

\(=\left(3x^4-3x^3\right)+\left(9x^3-9x^2\right)+\left(2x^2-2x\right)+\left(10x-10\right)\)

\(=\left(x-1\right)\left(3x^3+9x^2+2x+10\right)\)

Bài này đúng đề không

\(4x^4+2x^3-8x^2+3x+9\)

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

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

\(=\left(x+1\right)\left(4x^3+6x^2-8x^2-12x+6x+9\right)\)

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

Mình ko thêm bớt hạng tử nhé.

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

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

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

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

\(=\left(2x-1\right)\left(4x^2+5x+1\right)\)

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

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

\(8x^3-3x+6x^2-1=\left(8x^3-12x^2+6x-1\right)+\left(18x^2-9x\right)\)

\(=\left(\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2-1^3\right)+\left(18x^2-9x\right)\)

\(=\left(2x-1\right)^3+9x\left(2x-1\right)=\left(2x-1\right)\left(\left(2x-1\right)^2+9x\right)\)

\(=\left(2x-1\right)\left(4x^2-4x+1+9x\right)=\left(2x-1\right)\left(4x^2+5x+1\right)\)

=(3x^4-3x^3)+(5x^3-5x^2)-(3x^2-3x)-(5x-5)=3x^3(x-1)+5x^2(x-1)-3x(x-1)-5(x-1)=(x-1)(3x^3+5x^2-3x-5)=(x-1){x^2(3x+5)-(3x+5)}=(x-1)(3x+5)(x-1)(x+1)=(x-1)^2(3x+5)(x+1)

tham khảo câu hỏi tương tự nha bạn

a) \(x^2+4x+3=\left(x^2+4x+4\right)-1=\left(x+2\right)^2-1^2=\left(x+1\right)\left(x+3\right)\) (mình sửa lại)

b) \(x^2+8x-9=\left(x^2+8x+16\right)-25=\left(x+4\right)^2-5^2=\left(x-1\right)\left(x+9\right)\)

c) \(3x^2+6x-9=3\left[\left(x^2+2x+1\right)-4\right]=3\left[\left(x+1\right)^2-2^2\right]=3\left(x-1\right)\left(x+3\right)\)

d) \(2x^2+x-3=2x^2-4x+2+5x-5=2\left(x^2-2x+1\right)+5\left(x-1\right)=2\left(x-1\right)^2+5\left(x-1\right)=\left(x-1\right)\left(2x+3\right)\)

tik nhé

​

a) 6x^2-11x+3                              b)2x^2+3x-27                      c)3x^2-8x+4

= 6x^2-2x-9x+3                            =2x^2-6x+9x-27                    =3x^2-6x-2x+4

=2x(3x-1)-3(3x-1)                         =2x(x-3)+9(x-3)                      =3x(x-2)-2(x-2)

=(2x-3)(3x-1)                               =(2x+9)(x-3)                           =(3x-2)(x-2)      

\(f,x^3+3x^2+6x+4=x^3+x^2+2x^2+2x+4x+4\)

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

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

\(g,x^3-5x^2+8x-4=x^3-x^2-4x^2+4x+4x-4\)

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

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

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

      \(x^3-x^2-14x+24\)

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

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

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

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

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

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

      \(x^4+x^3+2x-4\)

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

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

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

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

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

      \(8x^4-2x^3-3x^2-2x-1\)

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

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

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

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

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

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

      \(3x^2-7x+2\)

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

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

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

Chúc bạn học tốt.