a) ( x 2  – 4x + 1)( x 2  – 2x + 3).

b) ( x 2  + 5x – 1)( x 2  + x – 1).

\(x^4-6x^3+12x^2-14x+3\) 

= \(x^4-4x^3+x^2-2x^3+8x^2-2x+3x^2-12x+3\) 

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

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

\(=x^4-4x^3+x^2-2x^3+8x^2-2x+3x^2-12x+3\)

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

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

c: \(x^4+x^3-4x^2+x+1\)

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

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

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

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

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

x⁴-6x³+12x²-14x+3 = (x² - 4x + 1) (x² - 2x + 3) 

x⁴-6x³+12x²-14x+3=x⁴-2x³+3x²-4x³+8x²-12x+x²-2x+3

=x²(x²-2x+3)-4x(x²-2x+3)+(x²-2x+3)

=(x²-2x+3)(x²-4x+1)

KO LÀM ĐC

vào cốc cốc math cứ thế ấn, nó sẽ ra nghiệm

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

= \(5x^3-2x^2-10x^2+4x+10x-4\)

= \(5x^2\left(x-\frac{2}{5}\right)-10x\left(x-\frac{2}{5}\right)+10\left(x-\frac{2}{5}\right)\)

=\(\left(x-\frac{2}{5}\right)\left(5x^2-10x+10\right)\)

Chuc ban hoc tot!

a. 3xy( 4x + y - \(\dfrac{4}{3}\) )

b. 2x²( 3x + 1 )

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

d. xy( 1 - x )( x - 1 )

e. 6( 2x + 1 )( x + y )