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b,(x2-11x+28)(x2-7x+10)-72
(x-4)(x-7)(x-2)(x-5)-72
(x-2)(x-7)(x-4)(x-5)-72
(x2-9x+14)(x2-9x+20)-72
Đặt"t"=x2-9x+14, ta có:
(=)t(t+6)-72
(=)t2+6t-72
(=)t2+12t-6t-72
(=)t(t-6)-12(t-6)
(=)(t-6)(t-12)
(=)(x2-9x+14-6)(x2-9x+14-12)
(=)(x2-9x+8)(x2-9x+2)
c: \(=4x^3-3x^2+4x^2-3x+4x-3=\left(4x-3\right)\left(x^2+x+1\right)\)
b: \(=\left(x-4\right)\left(x-7\right)\left(x-2\right)\left(x-5\right)-72\)
\(=\left(x^2-9x+20\right)\left(x^2-9x+14\right)-72\)
\(=\left(x^2-9x\right)^2+34\left(x^2-9x\right)+208\)
\(=\left(x^2-9x+26\right)\left(x^2-9x+8\right)\)
\(=\left(x-1\right)\left(x-8\right)\left(x^2-9x+26\right)\)
x2-7x+12
=x2-3x-4x+12
=x(x-3)-4(x-3)
=(x-3)(x-4)
x4-4x2+4x-1
=x4-1-4x2+4x
=(x2-1)(x2+1)-4x(x-1)
=(x-1)(x+1)(x2+1)-4x(x-1)
=(x-1)[(x+1)(x2+1)-4x]
=(x-1)(x3+x2+x+1-4x)
=(x-1)(x3+x2-3x+1)
6x4-11x2+3
=6x4-2x2-9x2+3
=2x2(3x2-1)-3(3x2-1)
=(3x2-1)(2x2-3)
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 \(x^2+6x+8=a\) )
\(=a^2+a-12=(a-3)(a+4)=(x^2+6x+5)(x^2+6x+12)\)
\(=(x+1)(x+5)(x^2+6x+12)\)