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

b) 3x⁴-3x³+9x³-9x²-24x²+24x-48x+48

=3x³(x-1)+9x²(x-1)-24x(x-1)-48(x-1)

=(x-1)(3x³+9x²-24x-48)

=3(x-1)(x³+3x²-8x-16)

b. 2x³-3x²+3x-1=2x³-x²-2x²+x+2x-1

= x²(2x-1)-x(2x-1)+(2x-1)

=(2x-1)(x²-x-1)

c. 3x³-14x²+4x+3= 3x³+x²-15x²-5x+9x+3

=x²(3x+1)-5x(3x-1)+3(3x+1)

=(3x+1)(x²-5x+3)

\(3x^3+5x^2-14x+4\\ =\left(3x^3-x^2\right)+\left(6x^2-2x\right)-\left(12x-4\right)\\ =x^2\left(3x-1\right)+2x\left(3x-1\right)-4\left(3x-1\right)\\ =\left(x^2+2-4\right)\left(3x-1\right)\)

a) \(-4x^2+10xy-14x\)

\(=2x\left(-2x+5y-7x\right)\)

b) \(3x\left(x-1\right)-y\left(1-x\right)+2x-2\)

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

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

Bài làm

a) -4x² + 10xy - 14x

= 2x( -2x + 5y - 7 )

b) 3x( x - 1 ) - y ( 1 - x ) + 2x - 2

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

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

# Học tốt #

\(2x^4-3x^3-14x^2-x+10\)

\(=\left(2x^4-4x^3-10x^2\right)+\left(x^3-2x^2-5x\right)-2x^2+4x+10\)

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

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

   x³ + x² + 4
= x³ + 2x² - x² - 2x + 2x + 4
= x²(x + 2) - x(x + 2) + 2(x + 2)
= (x + 2)(x² - x + 2)

   2x³ - 3x² + 3x - 1
= 2x³ - x² - 2x² + x + 2x - 1
= 2x²(x - 1/2) - 2x(x - 1/2) + 2(x - 1/2)
= (x - 1/2)(2x² - 2x + 2)
= 2(x - 1/2)(x² - x + 1)

   3x³ - 14x² + 4x + 3
= 3x³ + x² - 15x² - 5x + 9x + 3
= 3x²(x + 1/3) - 15x(x + 1/3) + 9(x + 1/3)
= (x + 1/3)(3x² - 15x + 9)
= 3(x + 1/3)(x² - 5x + 3)