x⁴-x³-x²+1

=x³(x-1)-(x²-1)

=x³(x-1)-(x-1)(x+1)

=(x-1)(x³-x-1)

x⁴ + x³ + x +1

= x³(x+1) + (x+1)

=(x+1)(x³ +1)

= (x+1)(x+1)(x² - x-1)

= (x+1)²(x² -x+1) 

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

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

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

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

(-x+6)(-x-2)

= -(x-6) . [- (x+2)]

= (x-6)(x+2)

= x(x+2) - 6(x+2)

= x² + 2x - 6x - 12

= x² - 4x -12

(2x-3)(5-x)

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

= 10x - 2x² - 15 + 3x

= -2x² - 15 + 13x

\(\left(2x-3\right)\left(5-x\right)=10x-2x^2-15+3x\)

\(=13x-2x^2-15\)

x³ - 3x² - 4x + 12

= x²(x-3) - 4(x-3)

= (x-3)(x² -4)

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

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

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

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

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

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

x² - 4x -5

= x² - 5x + x -5

= x(x-5) + (x-5)

=(x+1)(x-5)

x^2-4x-4=x²-2.2.x-2²

           =[x-2]²

Lần sau bạn phải ghi cả đề ra chứ -.-

x³ - 3x² + 1 - 3x

= x³ + x² - 4x² -4x + x +1

=x²(x+1) -4x(x+1) + (x+1)

=(x+1)(x² - 4x+1) 

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

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

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

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

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

2x² + 7x + 5

= 2x² + 2x + 5x + 5

= 2x(x+1) + 5(x+1)

=(2x+5)(x+1) 

16 - 5x² -3

= (16-3) - 5x²

= 13 - 5x²