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<=> 3x^5(x-3) - 4x^4(x-3) + 7x^3(x-3) - 5x^2(x-3) + 4x(x-3) - (x-3) = 0
<=> (x-3)(3x^5 - 4x^4 + 7x^3 - 5x^2 + 4x - 1) = 0
<=> (x-3)[3x^4(x-1/3) - 3x^3(x-1/3) + 6x^2(x-1/3) - 3x(x-1/3) + 3(x-1/3)] = 0
<=> (x-3)(x-1/3)(3x^4 - 3x^3 + 6x^2 - 3x + 3) = 0
<=> (x-3)(x-1/3)[3(x^4+2x^2+1) - 3x(x^2+1)] = 0
<=> (x-3)(x-1/3)(x^2+1)[3(x^2+1) - 3x] = 0
<=> 3(x-3)(x-1/3)(x^2+1)(x^2+1-x) = 0
....
a: \(\left(19x^2-14x^3+9-20x+2x^4\right):\left(1+x^2-4x\right)\)
\(=\left(2x^4-14x^3+19x^2-20x+9\right):\left(x^2-4x+1\right)\)
\(=\left(2x^4-8x^3+2x^2-6x^3+24x^2-6x-7x^2+28x-7-42x+16\right)\) :\(\left(x^2-4x+1\right)\)
\(=2x^2-6x-7+\frac{-42x+16}{x^2-4x+1}\)
b: \(\left(3x^4-2x^3-2x^2+4x+8\right):\left(x^2-2\right)\)
\(=\left(3x^4-6x^2-2x^3+4x+4x^2-8+16\right):\left(x^2-2\right)\)
\(=3x^2-2x+4+\frac{16}{x^2-2}\)
c: \(\left(2x^3-26x-24\right):\left(x^2+4x+3\right)\)
\(=\left(2x^3+8x^2+6x-8x^2-32x-24\right):\left(x^2+4x+3\right)\)
=2x-8
a) 6x3 + 3x2 + 4x + 2
= ( 6x3 + 3x2 ) + ( 4x + 2 )
= 3x2( 2x + 1 ) + 2( 2x + 1 )
= ( 2x + 1 )( 3x2 + 2 )
=> ( 6x3 + 3x2 + 4x + 2 ) : ( 3x2 + 2 ) = 2x + 1
b) 2x3 - 26x - 24
= 2( x3 - 13x - 12 )
= 2( x3 + 4x2 - 4x2 + 3x - 16x - 12 )
= 2[ ( x3 + 4x2 + 3x ) - ( 4x2 + 16x + 12 ) ]
= 2[ x( x2 + 4x + 3 ) - 4( x2 + 4x + 3 ) ]
= 2( x2 + 4x + 3 )( x - 4 )
=> ( 2x3 - 26x - 24 ) : ( x2 + 4x + 3 ) = 2( x - 4 ) = 2x - 8
c) x3 - 7x + 6
= x3 - 3x2 + 3x2 + 2x - 9x - 6
= ( x3 - 3x2 + 2x ) + ( 3x2 - 9x + 6 )
= x( x2 - 3x + 2 ) + 3( x2 - 3x + 2 )
= ( x2 - 3x + 2 )( x + 3 )
=> ( x3 - 7x + 6 ) : ( x + 3 ) = x2 - 3x + 2
a,\(\left(6x^3+3x^2+4x+2\right)\div\left(3x^2+2\right)\)
\(=\left[3x^2\left(2x+1\right)+2\left(2x+1\right)\right]\div\left(3x^2+2\right)\)
\(=\left[\left(3x^2+2\right)\left(2x+1\right)\right]\div\left(3x^2+2\right)\)
\(=2x+1\)