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)
