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

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

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

Đặt \(x^2+7x=t\)

\(\Rightarrow BT=\left(t+10\right)\left(t+12\right)-24\)

\(=t^2+22x+96=\left(t+11\right)^2-25\ge-25\)

Vậy GTNN của bt là - 25\(\Leftrightarrow x^2+7x+11=0\)

\(\Delta=7^2-4.11=5\)

\(\orbr{\begin{cases}x_1=\frac{-22+\sqrt{5}}{2}\\x_2=\frac{-22-\sqrt{5}}{2}\end{cases}}\)

2) \(\left(x-1\right)\left(x-3\right)\left(x-5\right)\left(x-7\right)-20\)

\(=\left(x-1\right)\left(x-7\right)\left(x-3\right)\left(x-5\right)-20\)

\(=\left(x^2-8x+7\right)\left(x^2-8x+15\right)-20\)

Đặt \(x^2-8x=t\)

\(\RightarrowĐT=\left(t+7\right)\left(t+15\right)-20\)

\(=t^2+22t+85=\left(t+11\right)^2-36\ge-36\)

Vậy GTNN của bt là - 36\(\Leftrightarrow x^2-8x+11=0\)

\(\Delta=\left(-8\right)^2-4.11=20\)

\(\orbr{\begin{cases}x_1=\frac{-22-\sqrt{20}}{2}\\x_2=\frac{-22+\sqrt{20}}{2}\end{cases}}\)

Nhầm, lộn tìm GTNN

a) \(\left(t+11\right)^2-25=\left(x^2+7x-16\right)\left(x^2+7x+36\right)\)

b) \(\left(x^2-8x+5\right)\left(x^2-8x+16\right)\)

\(=\left(x^2-8x+5\right)\left(x-4\right)^2\)

a)

\((6x+5)^2(3x+2)(x+1)-35\)

\(=(36x^2+60x+25)(3x^2+5x+2)-35\)

\(=[12(3x^2+5x+2)+1](3x^2+5x+2)-35\)

\(=(12a+1)a-35=12a^2+a-35\) (đặt \(3x^2+5x+2=a)\)

\(=4a(3a-5)+7(3a-5)=(4a+7)(3a-5)\)

\(=(12x^2+20x+15)(9x^2+15x+1)\)

b)

\(8(4x+1)(2x-3)(4x-3)(x+1)-130\)

\(=8[(4x+1)(4x-3)][(2x-3)(x+1)]-130\)

\(=8(16x^2-8x-3)(2x^2-x-3)-130\)

\(=8(8a+21)a-130\) (Đặt \(2x^2-x-3=a\) )

\(=64a^2+168a-130=2(8a-5)(4a+13)\)

\(=2(8x^2-4x+1)(16x^2-8x-29)\)

c)

\((4x+1)(12x-1)(3x+2)(x+1)-4\)

\(=[(4x+1)(3x+2)][(12x-1)(x+1)]-4\)

\(=(12x^2+11x+2)(12x^2+11x-1)-4\)

\(=(a+2)(a-1)-4\) (đặt \(a=12x^2+11x\) )

\(=a^2+a-6=(a-2)(a+3)\)

\(=(12x^2+11x-2)(12x^2+11x+3)\)

d)

\((x+2)(x+3)^2(x+4)-12\)

\(=[(x+2)(x+4)](x+3)^2-12\)

\(=(x^2+6x+8)(x^2+6x+9)-12\)

\(=a(a+1)-12\) (Đặt \(x^2+6x+8=a\) )

\(=a^2+a-12=(a-3)(a+4)=(x^2+6x+5)(x^2+6x+12)\)

\(=(x+1)(x+5)(x^2+6x+12)\)

e)

\((x^2+5x+6)(x^2-15x+56)-144\)

\(=(x+2)(x+3)(x-8)(x-7)-144\)

\(=[(x+2)(x-7)][(x+3)(x-8)]-144\)

\(=(x^2-5x-14)(x^2-5x-24)-144\)

\(=a(a-10)-144=a^2-10a-144\) (đặt \(x^2-5x-14=a\))

\(=(a-18)(a+8)=(x^2-5x-32)(x^2-5x-6)\)

\(=(x^2-5x-32)(x-6)(x+1)\)

g)

\((x^2-11x+28)(x^2-7x+10)-72\)

\(=(x-7)(x-4)(x-2)(x-5)-72\)

\(=[(x-7)(x-2)][(x-4)(x-5)]-72\)

\(=(x^2-9x+14)(x^2-9x+20)-72\)

\(=a(a+6)-72\) (Đặt \(x^2-9x+14=a\) )

\(=a^2+6a-72=(a-6)(a+12)\)

\(=(x^2-9x+8)(x^2-9x+26)\)

\(=(x-1)(x-8)(x^2-9x+26)\)