\(12x^2+7x-12=12x^2-5x+12x-12\)

\(=x\left(12x-5\right)+12\left(x-1\right)\)

Đề sai rồi bạn ời

\(12x^2+7x-12=\left(12x^2-9x\right)+\left(16x-12\right)=3x\left(4x-3\right)+4\left(4x-3\right)=\left(3x+4\right)\left(4x-3\right)\)

Phân tích đa thức sau thành nhân tử 7x^2 +12x+5 

f)\(x^2-5x-14=x^2-7x+2x-14=x\left(x-7\right)+2\left(x-7\right)=\left(x-7\right)\left(x+2\right)\)

i)\(x^2-7x+10=x^2-2x-5x+10=x\left(x-2\right)-5\left(x-2\right)=\left(x-5\right)\left(x-2\right)\)

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

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

f)\(x^2-5x-14=x^2-7x+2x-14\)

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

i)\(x^2-7x+10=x^2-5x-2x+10\)

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

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

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

g)\(x^2+6x+5=x^2+x+5x+5\)

                           \(=\left(x+5\right)\left(x+1\right)\)

f) \(x^2-5x-14\)

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

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

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

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

i) \(x^2-7x+10\)

\(=x^2-5x-2x+10\)

\(=\left(x^2-5x\right)-\left(2x-10\right)\)

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

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

h) \(x^2-7x+12\)

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

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

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

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

g) \(x^2+6x+5\)

\(=x^2+x+5x+5\)

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

\(=x\left(x+1\right)+5\left(x+1\right)\)

\(=\left(x+5\right)\left(x+1\right)\)

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

b)\(3x^2+9x-30=3x^2-6x+15x-30=3\left(x-2\right)\left(x+5\right)\)

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

d)\(x^2-7x+10=x^2-2x-5x+10=\left(x-2\right)\left(x-5\right)\)

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

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

b) \(3x^2+9x-30=3\left(x^2+3x-10\right)=3\left(x^2-2x+5x-10\right)\)

\(=3\left[\left(x^2-2x\right)+\left(5x-10\right)\right]=3\left[x\left(x-2\right)+5\left(x-2\right)\right]\)

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

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

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

d) \(x^2-7x+10=x^2-2x-5x+10=\left(x^2-2x\right)-\left(5x-10\right)\)

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

a,\(x^2-5x+6=x^2-2x-3x+6 =x(x-2)-3(x-2) =(x-2)(x-3)\)

b,\(3x^2+9x-30=3x^2+15x-6x-30=3x(x+5)-6(x+5)=(x+5)(3x-6)\)

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

d,\(x^2-7x+10=x^2-2x-5x+10=x(x-2)-5(x-2)=(x-2)(x-5)\)

Hok tốt !!!!!!!!!!

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

a) \(x^3+4x^2-21x\)

\(=x\left(x^2+4x-21\right)\)

\(=x\left(x^2-3x+7x-21\right)\)

\(=x\left[x\left(x-3\right)+7\left(x-3\right)\right]\)

\(=x\left(x-3\right)\left(x+7\right)\)

b) \(5x^3+6x^2+x\)

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

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

\(=x\left[5x\left(x+1\right)+\left(x+1\right)\right]\)

\(=x\left(x+1\right)\left(5x+1\right)\)

c) \(x^3-7x+6\)

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

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

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

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

d) \(3x^3+2x-5\)

\(=3x^3+3x^2+5x-3x^2-3x-5\)

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

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

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

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

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

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

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

a) x⁴ + 3x² + 4

= [ ( x² )² + 4x² + 2² ] - x²

= ( x² + 2 )² - x²

= ( x² + 2 - x² ).( x² + 2 + x² )

= 2( 2x² + 2 )

b) x⁴ + 5x² + 9

= [ ( x² )² + 6x² + 3² ] - x²

= ( x² + 3 )² - x²

= ( x² + 3 - x² )( x² + 3 + x² )

= 3( 2x² + 3 )

a) \(=x^2-2x-4x+8\)

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

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

c) \(=x^3-x-6x-6\)

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

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

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

\(=x\left(x+1\right)\left(x-7\right)\)