Đáp án:
Giải thích các bước giải:
a) (x ^2+x)^2+4*(x^2+x)-12
<=>x^4 + 2x^3 + x^2 + 4x^2 + 4x - 12
<=>x^4 + 2x^3 + 5x^2 + 10x - 6x - 12
<=>x^3(x+2) + 5x(x+2)-6(x+2)
<=>(x+2)(x^3 + 5x - 6)
<=>(x+2)(x^3 - x+ 6x - 6)
<=>(x+2)[(x-1)(x^2+x+1) + 6(x-1)]
<=>(x+2)(x-1)(x^2+x+7)
d) x^4+4*x^2-5
=[(x^2)^2+4x^2+4]-9
=(x^2+2)^2-3^2
=(x^2+2-3)(x^2+2+3)
=(x^2-1)(x^2+5)
e) x^8+x^7+1
=x^8+x^7+x^6-x^6+1
=x^6(x^2+x+1)-[(x^3)^2-1]
=x^6(x^2+x+1)-(x^3-1)(x^3+1)
=x^6(x^2+x+1)-(x-1)(x^2+x+1)(x^3+1)
=(x^2+x+1)[x^6-(x-1)(x^3+1)]
=(x^2+x+1)[x^6-(x^4+x-x^3-1)]
=(x^2+x+1)[x^6-x^4-x+x^3+1)]
f) x^4+2*x^2-24
Đặt t=x^2
=t^2+2t-24
=t^2-4t+6t-24
=t(t-4)+6(t-4)
=(t+6)(t-4)
=(x^2+6)(x^2-4)
=(x^2+6)(x-2)(x+2)
g) 2*x^2+10*x+8
=2x^2+2x+8x+8
=2x(x+1)+8(x+1)
=(2x+8)(x+1)
h) 4*x^2-36*x+56
i) x^3-5*x^2-14*x
=x^3+2x^2-7x^2-14x
=(x^3+2x^2)-(7x^2+14x)
=x^2(x+2)-7x(x+2)
=(x^2-7x)(x+2)
