Question

( x + 1 )( x + 3 )( x + 5 )( x + 7 ) + 15

Phân tích đa thức thành nhân tử:

Answer 1

\(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)

\(=\left(x+1\right)\left(x+7\right)\left(x+3\right)\left(x+5\right)+15\)

\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)

Đặt \(x^2+8x+11=t\) , ta có :

\(\left(t-4\right)\left(t+4\right)+15\)

\(=t^2-16+15=t^2-1\)

\(=\left(t-1\right)\left(t+1\right)\)

\(=\left(x^2+8x+11-1\right)\left(x^2+8x+11+1\right)=\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)

Answer 2

Ta có:A=(x+1)(x+3)(x+5)(x+7)+15

=[(x+1)(x+7)][(x+3)(x+5)]+15

=(x²+8x+7)(x²+8x+15)+15

Đăt:t=x²+8x+7

Khi đó:A=t(t+8)+15

=>A=t²+8t+15=>A=(t+3)(t+5)

hay A=(x²+8x+10)(x²+8x+12)