Question

Phân tích thành nhân tử:

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

b/(4x+1)(12x-1)(3x+2)(x+1)-4

c/4(x+5)(x+6)(x+10)(x+12)-3x²

Answer 1

a, \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

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

\(=\left(x^2+5x+2x+10\right)\left(x^2+4x+3x+12\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)(1)

Đặt \(x^2+7x+10=a\Rightarrow x^2+7x+12=a+2\)

Thay vào (1) ta được:

\(a\left(a+2\right)-24=a^2+2a-24\)

\(=a^2-4a+6a-24=a.\left(a-4\right)+6.\left(a-4\right)\)

\(=\left(a-4\right).\left(a+6\right)\)(*)

Vì \(x^2+7x+10=a\) nên

(*) \(=\left(x^2+7x+10-4\right)\left(x^2+7x+10+6\right)\)

\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)

\(=\left(x^2+x+6x+6\right)\left(x^2+7x+16\right)\)

\(=\left[x.\left(x+1\right)+6.\left(x+1\right)\right]\left(x^2+7x+16\right)\)

\(=\left(x+1\right).\left(x+6\right).\left(x^2+7x+16\right)\)

Các câu còn lại làm tương tự! Chúc bạn học tốt!!!