Ta có: \(\left(48x^2+8x-1\right)\left(3x^2+5x+2\right)-4\)

    \(=\left[\left(48x^2-4x\right)+\left(12x-1\right)\right]\left[\left(3x^2+3x\right)+\left(2x+2\right)\right]-4\)

    \(=\left[4x.\left(12x-1\right)+\left(12x-1\right)\right]\left[3x.\left(x+1\right)+2.\left(x+1\right)\right]-4\)

    \(=\left(4x+1\right).\left(12x-1\right)\left(3x+2\right).\left(x+1\right)-4\)

    \(=\left[\left(4x+1\right)\left(3x+2\right)\right]\left[\left(12x-1\right)\left(x+1\right)\right]-4\)

    \(=\left(12x^2+11x+2\right)\left(12x^2+11x-1\right)-4\)

Gọi \(a=12x^2+11x-1\)\(\Rightarrow\)\(a+3=12x^2+11x+2\)

Ta lại có: \(\left(a+3\right).a-4=a^2+3a-4\)

                                               \(=\left(a^2-a\right)+\left(4a-4\right)\)

                                               \(=a.\left(a-1\right)+4.\left(a-1\right)\)

                                               \(=\left(a+4\right).\left(a-1\right)\)

                                               \(=\left(12a^2+11x-1+4\right).\left(12a^2+11-1-1\right)\)

                                               \(=\left(12a^2+11x+3\right).\left(12a^2+11-2\right)\)

\(a,x^4+5x^3-8x-40=x^3\left(x+5\right)-8\left(x+5\right)\\ =\left(x^3-8\right)\left(x+5\right)=\left(x-2\right)\left(x^2+2x+4\right)\left(x+5\right)\\ b,3x^2-6x-12y^2+3=3\left(x^2-2x-4y^2+1\right)\\ =3\left[\left(x-1\right)^2-4y^2\right]=3\left(x-2y-1\right)\left(x+2y-1\right)\)

\(x^4+8x^3+28x^2+48x-13\)

\(=x^4+4x^3+13x^2+4x^3+16x^2+52x-x^2-4x-13\)

\(=x^2\left(x^2+4x+13\right)+4x\left(x^2+4x+13\right)-\left(x^2+4x+13\right)\)

\(=\left(x^2+4x-1\right)\left(x^2+4x+13\right)\)

\(a,3x-15xy=3x\left(1-5y\right)\\ ---\\ 8x^2+6x-4=2\left(4x^2+3x-2\right)\\ ---\\ 5x^2+25xy+10y^2=5\left(x^2+5xy+2y^2\right)\\ ---\\ 9x^2y^2+6x^2y-\dfrac{1}{2}xy^2=\dfrac{1}{2}xy\left(18xy+12x-y\right)\)

Phân tích đa thức thành nhân tử(tách hạng tử)
1)x^2+2x-3=x^2-x+3x-3=x(x-1)+3(x-1)=(x-1)(x+3)
2)x^2-5x+6=x^2-2x-3x+6=x(x-2)-3(x-2)=(x-2)(x-3)
3)x^2+7x+12=(x+3)(x+4)
4)x^2-x-12=(x-4)(x+3)
5)3x^2+3x-36=3[(x-3)(x+4)]
6)5x^2-5x-10=5[(x-2)(x+1) ]       
7)3x^2-7x-6=(x-3)(3x+2)
8)4x^2+4x-3=4x^2+6x-2x-3=(2x-1)(2x+3)
9)8x^2-2x-3=8x^2+4x-6x-3=(4x-3)(2x+1)
 

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

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

3: \(x^2+7x^2+12x=4x\left(2x+3\right)\)

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

5: \(3x^2+3x-36=3\left(x^2+x-12\right)=3\left(x+4\right)\left(x-3\right)\)

6: \(5x^2-5x-10=5\left(x^2-x-2\right)=5\left(x-2\right)\left(x+1\right)\)