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 !!!!!!!!!!

a) x³ - 7x + 6

= x³ - 2x² + 2x² - 4x - 3x + 6

= x² ( x - 2 ) + 2x ( x - 2 ) - 3 ( x - 2 )

= ( x - 2 ) ( x² + 2x - 3 )

= ( x - 2 ) ( x² - x + 3x - 3 )

= ( x - 2 ) [ x ( x - 1 ) + 3 ( x - 1 ) ] 

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

b ) x³ - 9x² + 6x + 16

= x³ - 8x² - x² + 8x - 2x + 16

= x² ( x - 8 ) - x ( x - 8 ) - 2 ( x - 8 )

= ( x - 8 ) ( x² - x - 2 )

= ( x - 8 ) ( x² + x - 2x - 2 )

= ( x - 8 ) [ x ( x + 1 ) - 2 ( x + 1 ) ]

= ( x - 8 ) ( x + 1 ) ( x - 2 )

c ) x³ - 6x² - x + 30

= x³ - 5x² - x² + 5x - 6x + 30

= x² ( x - 5 ) - x ( x - 5 ) - 6 ( x - 5 )

= ( x - 5 ) ( x² - x - 6 )

= ( x - 5 ) ( x² - 3x + 2x - 6 )

= ( x - 5 ) [ x ( x - 3 ) + 2 ( x - 3 ) ]

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

d ) 2x³ - x² + 5x + 3

= 2x³ + x² - 2x² - x + 6x + 3

= x² ( 2x + 1 ) - x ( 2x + 1 ) + 3 ( 2x + 1 )

= ( 2x + 1 ) ( x² - x + 3 )

\(x=-10\) hoặc \(x=3\)

\(\Leftrightarrow x^2+10x-3x-30=0\\ \Leftrightarrow x\left(x+10\right)-3\left(x+10\right)=0\\ \Leftrightarrow\left(x+10\right)\left(x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-10\\x=3\end{matrix}\right.\)

\(x^4-14x^2-7x+30=\left(x^4+x^3-3x^2\right)+\left(-x^3-x^2+3x\right)+\left(-10x^2-10x+30\right)\)

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

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

x^4-14*x^2-7*x+30=(x^2-x-10)*(x^2+x-3)

a) a⁴ + a² - 2

a⁴ + 2a² - a² - 2

a².( a² + 2 ) - ( a² + 2 )

( a² - 1 ).( a² + 2 )

( a + 1 ).( a - 1 ).( a² +2 )

b) x⁴ + 4x² - 5

x⁴ + 5x² - x² - 5

x².( x² + 5 ) - ( x² + 5 )

( x² - 1 ).( x² + 5 )

( x + 1 ).( x - 1 ).( x² + 5 )

c) x³ - 19x - 30

x³ + 2x² - 2x² + 4x - 15x - 30

x²( x + 2 ) - 2x.( x + 2 ) - 15.( x + 2 )

( x + 2 ).( x² - 2x - 15 )

d) x³ - 7x - 6

x³ - 3x² + 3x² - 9x + 2x - 6

x².( x - 3 ) + 3x.( x - 3 ) + 2.( x - 3 )

( x - 3 ).( x² + 3x +2 )

( x - 3 ).( x² + 2x + x + 2 )

( x - 3 ).( x.( x + 2 ) + ( x + 2 )

( x + 1 ).( x + 2 ).( x - 3 )

e) x³ - 5x² - 14x

x³ - 7x² + 2x² - 14x

x².( x - 7 ) + 2x.( x - 7 )

( x - 7 ).( x² + 2x )

x.( x + 2 ).( x - 7 )

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

\(x^3-19x-30=x^3+6x-25x-30=x\left(x^2-25\right)+6x-30=x\left(x^2-25\right)+6\left(x-5\right)\)

\(=x\left(x-5\right)\left(x+5\right)+6\left(x-5\right)=\left(x-5\right)\left[\left(x\right)\left(x+5\right)+6\right]\)

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

\(c,x^2-3x+2\\=x^2-x-2x+2\\=x(x-1)-2(x-1)\\=(x-1)(x-2)\\---\\d,3x^2-5x-2\\=3x^2-6x+x-2\\=3x(x-2)+(x-2)\\=(x-2)(3x+1)\\Toru\)

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

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

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

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

b )

\(x^3-19x-30=\left(x^3-9x\right)-\left(10x+30\right)=x\left(x^2-9\right)-10\left(x+3\right)\)

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

c )

\(a^3-6a^2+11a-6=\left(a-3\right)\left(a-2\right)\left(a-1\right).\)