Đáp án:
Giải thích các bước giải:
câu 5
a, (a+1)(a+3)(a+5)(a+7)+15
=(a^2+a+7a+7)(a^2+3a+5a+15)+15
=(a^2+8a+7)(a^2+8a+15)+15
Dặt t=a^2+8a+11 ta có
(t-4)(t+4)+15
=t^2-16+15
=t^2-1=(t-1)(t+1)(a^2+8a+11-1)(a^2+8a+11+1)
=(a^2+8a+10)(a^2+8a+12)
b,x^4+2010x^2+2009x+2010
=(x^4-x^3+2010x^2)+(x^3-x^2=2010x)+x^2-x+2010)
=x^2(x^2-x+2010)+x(x^2-x+2010)+(x^2-x+2010)
=(x^2+x+1)(x^2-x+2010)
c, (x+2)(x+3)(x+4)(x+5)-24
=(x^2+2x+5x+10)(x^2+3x+4x+12)-24
=(x^2+7x+10)(x^2+7x+12)-24
Đặt t=x^2+7x+11 ta có
(t-1)(t+1)-24
=t^2-1-24
=(t-5)(+5)
=(x^2+7x+11-5)(x^2+7x+11+5)
=(x^2+7x+6)(x^2+7x+16)
