5) x³ + x² - 3x - 27
= (x³ - 27) + (x² - 3x)
= (x - 3)(x² + 3x + 9) + x(x - 3)
= (x - 3)(x² + 3x + 9 + x)
= (x - 3)(x² + 4x + 9)
6) x³ + x² - 4x - 4)
= (x³ + x²) - (4x + 4)
= x²(x + 1) - 4(x + 1)
= (x + 1)(x² - 4)
= (x + 1)(x + 2)(x - 2)
7) x² - 9x - 9y - y²
= (x² - y²) - (9x + 9y)
= (x - y)(x + y) - 9(x + y)
= (x + y)(x - y - 9)
8) y⁴ - 3y³ + 3y² - y
= y(y³ - 3y² + 3y - 1)
= y(y - 1)³
Lời giải:
5.
$x^3+x^2-3x-27=(x^3-27)+(x^2-3x)=(x^3-3^3)+(x^2-3x)$
$=(x-3)(x^2+3x+9)+x(x-3)=(x-3)(x^2+3x+9+x)=(x-3)(x^2+4x+9)$
6.
$x^3+x^2-4x-4=(x^3-4x)+(x^2-4)=x(x^2-4)+(x^2-4)=(x^2-4)(x+1)$
$=(x-2)(x+2)(x+1)$
7.
$x^2-9x-9y-y^2=(x^2-y^2)-(9x+9y)=(x-y)(x+y)-9(x+y)$
$=(x+y)(x-y-9)$
8.
$y^4-3y^3+3y^2-y=(y^4-y)-(3y^3-3y^2)$
$=y(y^3-1)-3y^2(y-1)=y(y-1)(y^2+y+1)-3y^2(y-1)$
$=(y-1)[y(y^2+y+1)-3y^2]=(y-1)(y^3-2y^2+y)$
$=y(y-1)(y^2-2y+1)=y(y-1)(y-1)^2=y(y-1)^3$
