1/ Tách 1 hạng tử thành nhiều hạng tử

a)a^4+a²+1

= a^4 - a + a² + a + 1

= (a^4 - a) + (a² + a + 1)

= a(a - 1)(a² + a + 1) + (a² + a + 1)

= (a² + a + 1)(a² - a + 1)

b)a^4 + a² - 2

= a^4 - a³ + a³ - a² + 2a² - 2a + 2a - 2

= (a^4 - a³) + (a³ - a²) + (2a² - 2a) + (2a - 2)

= a³(a - 1) + a²(a - 1) + 2a(a - 1) + 2(a - 1)

= (a - 1)(a³ + a² + 2a + 2)

= (a - 1)[(a³ + a²) + (2a + 2)]

= (a - 1)[a²(a + 1) + 2(a +1)]

= (a - 1)(a + 1)(a² + 2)

c)x^4 + 4x² - 5

= x^4 - x³ + x³ - x² + 5x² - 5x + 5x - 5

= (x^4 - x³) + (x³ - x²) + (5x² - 5x) + (5x - 5)

= x³(x - 1) + x²( x - 1) + 5x( x - 1) + 5( x - 1)

= (x - 1)(x³ + x² + 5x + 5)

= (x-1)[x²(x+1) + 5(x+1)]

= (x-1)(x+1)(x²+5)

d)x³-19x-30

= x³ + 2x² - 2x² - 4x - 15x - 30

= x²(x+2) - 2x(x+2) - 15(x+2)

= (x+2)(x² - 2x -15)

= (x+2)(x² + 3x - 5x - 15)

= (x+2)[x(x+3) - 5(x+3)]

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

e)x³-7x-6

= x³ - 3x² + 3x² - 9x + 2x - 6

= x²(x -3) + 3x(x-3) + 2(x-3)

= (x-3)(x² + 3x+2)

= (x-3)(x²+x+2x+2)

=(x-3)[x(x+1) + 2(x+1)]

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

f)x²yz+5xyz-14yz

= yz(x² + 5x - 14)

= yz(x² - 2x + 7x - 14)

= yz[x(x-2) + 7(x-2)]

= yz(x-2)(x+7)

2/ Thêm bớt cùng một hạng tử

a)x^4+4

=x^4 + 4x² + 4 - 4x²

= (x² + 2)² - (2x)²

= (x² + 2 - 2x)(x² + 2 + 2x)

b)x^4+64

= x^4 + 16x² + 64 - 16x²

= (x² + 8)² - (4x)²

= (x² - 4x + 8)(x² + 4x + 8)

c)x^8+x^7+1

= x^8 + x^7 + x^6 + x^5 + x^4 + x³ + x² + x - x^6 - x^5 - x^4 - x³ - x² - x + 1

= x^6(x²+x+1) + x³(x²+x+1) + (x² + x + 1) - x^4(x²+x+1)-x(x²+1+1)

= (x²+x+1)(x^6-x^4+x³-x+1)

d)x^8+x^4+1

= x^8 - x^5 + x^5 - x² + x^4 - x + x² + x + 1

= (x^8 - x^5) + (x^5 - x²) + (x^4 - x) + (x² + x + 1)

= x^5(x-1)(x²+x+1) + x²(x-1)(x²+x+1) + (x² + x + 1)

= (x²+x+1)(x^6-x^5 + x³ - x² + 1)

e)x^5+x+1

= x^5 - x² + x² + x + 1

= x²(x-1)(x²+x+1) + (x²+x+1)

=(x²+x+1)(x³-x²+1)

f)x³+x²+4

= x³ + 2x² - x² - 2x + 2x + 4

= x²(x+2) - x(x+2) + 2(x+2)

= (x+2)(x²-x+2)

g)x^4+2x²-24

= x^4 - 2x³ + 2x³ - 4x² + 6x² - 12x + 12x - 24

= x³(x-2) + 2x²(x-2) + 6x(x-2) + 12(x-2)

= (x-2)(x³ + 2x² + 6x + 12)

= (x-2)[x²(x+2) + 6(x+2)]

= (x-2)(x+2)(x²+6)

h)x³-2x-4

= x³ - 2x² + 2x² - 4x + 2x - 4

= x²(x-2) + 2x(x-2) + 2(x-2)

= (x-2)(x² + 2x + 2)

i)a^4+4ab^4

= a(a³ + 4b^4)