Question

Phân tích thành nhân tử: (x+2)(x +3)(x +4)(x +5) -24

Answer 1

(x+2)(x+3)(x+4)(x+5)-24

=\([\left(x+2\right)\left(x+5\right)].[\left(x+3\right)\left(x+4\right)]-24\)

=(x²+5x+2x+10)(x²+4x+3x+12)

=(x²+7x+10)(x²+7x+12)

Đặt x²+7x+10=t

\(\Rightarrow\)t(t+2)-24

\(\Leftrightarrow\)t²+2t-24

\(\Leftrightarrow\)t²+6t-4t-24

\(\)\(\Leftrightarrow\)t(t+6)-4(t+6)

\(\Leftrightarrow\)(t+6)(t-4)

Thay t=x²+7x+10 ta được

(x²+7x+10+6)(x²+7x+10-4)

\(\Leftrightarrow\)(x²+7x+16)(x²+7x+6)

\(\Leftrightarrow\)(x²+7x+16)(x²+x+6x+6)

\(\Leftrightarrow\)(x²+7x+16)x(x+1)6(x+1)

\(\Leftrightarrow\)(x²+7x+16)(x+1)(x+6)