\(3x^3-4x^2+13x-4\)

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

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

\(x^4+13x^2+36=x^4+4x^2+9x^2+36\)

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

       \(x^4+13x^2+36\)

<=> \(x^4+9x^2+4x^2+36\)

<=> \(x^2\left(x^2+9\right)+4\left(x^2+9\right)\)

<=> \(\left(x^2+9\right)\left(x^2+4\right)\)

\(x^4+13x^2+36\)

\(=x^4+4x^2+9x^2+36\)

\(=\left(x^4+4x^2\right)+\left(9x^2+36\right)\)

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

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

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

\(4x^3-13x^2+9x-18=4x^3-12x^2-x^2+3x+6x-18\)

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

\(4x^3-13x^2+9x-18\)

\(=4x^3-12x^2-x^2+3x+6x-18\)

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

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

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

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

c: \(x^2+8x+15=\left(x+5\right)\left(x+3\right)\)

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

e: \(x^2-13x+36=\left(x-9\right)\left(x-4\right)\)

\(12y-9x^2+36-3x^2y\)

\(=\left(36-9x^2\right)-\left(3x^2y-12y\right)\)

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

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

\(12y-9x^2+36-3x^2y\)

\(=\left(12y-3x^2y\right)-\left(9x^2-36\right)\)

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

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

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

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

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

=(−3)(x−2)(x+2)(3+y)

\(=\left(13x^2-13x\right)-\left(14x-14\right)=13x\left(x-1\right)-14\left(x-1\right)=\left(13x-14\right)\left(x-1\right)\)

THAM KHẢO NHÉ BẠN, MÌNH KO VT ĐC TRONG NÀY NÊN PHẢI RA WORD VÍT R COPY VÀO Á:

$7x^2-13x+6=0\iff 7x^2-7x-6x+6=0$

$\iff 7x\left(x-1\right)-6\left(x-1\right)=0\iff \left(7x-6\right)\left(x-1\right)=0$

x=1;x=67

`#040911`

`7x^2 - 13x + 6`

`= 7x^2 - 7x - 6x + 6`

`= (7x^2 - 7x) - (6x - 6)`

`= 7x(x - 1) - 6(x - 1)`

`= (7x - 6)(x - 1)`

\(7x^2-13x+6=7\left(x-1\right)\left(x-\dfrac{6}{7}\right)\)

\(=6x^2+3x+10x+5=3x\left(2x+1\right)+5\left(2x+1\right)=\left(3x+5\right)\left(2x+1\right)\)

6x2+3x+10x+5=3x(2x+1)+5(2x+1)=(3x+5)(2x+1)