Phân tích đa thức thành nhân tử
1) x^3 - 7x + 6
2) x^3 - 9x^2 + 6x + 16
3) x^3 - 6x^2 - x + 30
4) 2x^3 - x^2 + 5x + 3
5) 27x^3 - 27x^2 + 18x - 4
6) x^2 + 2xy + y^2 - x - y - 12
7) (x + 2)(x +3)(x + 4)(x + 5) - 24
8) 4x^4 - 32x^2 + 1
9) 3(x^4 + x^2 + 1) - (x^2 + x + 1)^2
10) 64x^4 + y^4
11) a^6 + a^4 + a^2b^2 + b^4 - b^6
12) x^3 + 3xy + y^3 - 1
13) 4x^4 + 4x^3 + 5x^2 + 2x + 1
14) x^8 + x + 1
15) x^8 + 3x^4 + 4
16) 3x^2 + 22xy + 11x + 37y + 7y^2 +10
17) x^4 - 8x + 63
đúng nhiều nhất sẽ đc tick
1
x3-7x+6
=x3+0x2-7x +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+3x-2x-6)
=(x-1)[x(x+3)-2(x+3)]
=(x-1)(x-2)(x+3)
7) (x+2)(x+3)(x+4)(x+5)-24
=(x+2)(x+5) (x+3)(x+4)-24
=[x(x+5)+2(x+5)][x(x+4)+3(x+4)]-24
=[x2+5x+2x+10][x2+4x+3x+12]-24
=[x2+7x+10][x2+7x+12]-24
đặt a=x2+7x+10
=>x2+7x+12=a+2
=a(a+2)-24
=a2+2a-24
=a2+6a-4a-24
=(a2+6a)-(4a+24)
=a(a+6)-4(a+6)
=(a+6)(a-4)
thay a= x2+7x+10 vào ta được
(x2+7x+10+6)(x2+7x+10-4)
=(x2+7x+16)(x2+7x+6)
