Question

Phân tích đa thức thành nhân tử:

a. (6x+5)² (3x+2) (x+1) - 35

b. 8(4x+1) (2x-3) (4x-3) (x+1) - 130

c. (4x+1) (12x-1) (3x+2) (x+1) -4

d. (x+2) (x+3)² (x+4) - 12

e. (x² +5x +6) (x² -15x +56) - 144

g. (x² -11x +28) (x² -7x+10) -72

Mình đang cần gấp mong các bạn giúp đỡ mình!

Answer 1

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 \(2x^2-x-3=a\) )

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

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

Answer 2

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 \(x^2+6x+8=a\) )

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

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

Answer 3

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 \(x^2-9x+14=a\) )

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

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

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