1) 6x² - 11x + 3
= 6x² - 2x - 9x + 3
= (6x² - 2x) - (9x - 3)
= 2x(3x - 1) - 3(3x - 1)
= (3x - 1)(2x - 3)
2) 2x² + 3x - 27
= 2x² - 6x + 9x - 27
= (2x² - 6x) + (9x - 27)
= 2x(x - 3) + 9(x - 3)
= (x - 3)(2x + 9)
3) 2x² + 3xy - 5y²
= 2x² - 2xy + 5xy - 5y²
= (2x² - 2xy) + (5xy - 5y²)
= 2x(x - y) + 5y(x - y)
= (x - y)(2x + 5y)
4) x³ - 7x - 6
= x³ + x² - x² - x - 6x - 6
= (x³ + x²) - (x² + x) - (6x - 6)
= x²(x + 1) - x(x + 1) - 6(x + 1)
= (x + 1)(x² - x - 6)
= (x + 1)(x² + 2x - 3x - 6)
= (x + 1)[(x² + 2x) - (3x + 6)]
= (x + 1)[x(x + 2) - 3(x + 2)]
= (x + 1)(x + 2)(x - 3)
5) 4x⁴ + 81
= 4x⁴ + 36x² + 81 - 36x²
= (4x⁴ + 36x² + 81) - 36x²
= (2x² + 9)² - (6x)²
= (2x² + 9 + 6x)(2x² + 9 - 6x)
= (2x² + 6x + 9)(2x² - 6x + 9)
7) Em xem lại đề nhé
8) x³ + y³ + z³ - 3xyz
= x³ + 3x²y + 3xy² + y³ + z³ - 3x²y - 3xy² - 3xyz
= (x³ + 3x²y + 3xy² + y³) + z³ - (3x²y + 3xy² + 3xyz)
= (x + y)³ + z³ - 3xy(x + y + z)
= (x + y + z)[(x + y)² - (x + y)z + z²] - 3xy(x + y + z)
= (x + y + z)(x² + 2xy + y² - xz - yz + z² - 3xy)
= (x + y + z)(x² + y² + z² - xy - xz - yz)
1: =6x^2-9x-2x+3
=3x(2x-3)-(2x-3)
=(2x-3)(3x-1)
2: =2x^2+9x-6x-27
=x(2x+9)-3(2x+9)
=(2x+9)(x-3)
3: =2x^2-2xy+5xy-5y^2
=2x(x-y)+5y(x-y)
=(x-y)(2x+5y)
4: =x^3-x-6x-6
=x(x-1)(x+1)-6(x+1)
=(x+1)(x^2-x-6)
=(x+1)(x-3)(x+2)
5: =4x^4+36x^2+81-36x^2
=(2x^2+9)^2-(6x)^2
=(2x^2-6x+9)(2x^2+6x+9)
6: =x^4+2x^2+1-x^2
=(x^2+1)^2-x^2
=(x^2-x+1)(x^2+x+1)
8: =(x+y)^3+z^3-3xy(x+y)-3xyz
=(x+y+z)(x^2+2xy+y^2-xz-yz+z^2)-3xy(x+y+z)
=(x+y+z)(x^2+y^2+z^2-xy-xz-yz)