2007-02-28 03:30:31 · 5 answers · asked by sikirutaye 1 in Science & Mathematics ➔ Mathematics
Ans: (x - 1) (x - 2) (x - 3) (x + 1)
x^4-5*x^3+5*x^2+5*x-6
= x^2 * (x^2 -5*x +5 ) + 5*x - 6
= x^2 * (x^2 -3*x -2*x +6 ) -x^2 + 5*x -6
= x^2 * (x *(x-3) -2 * (x-3) ) - x^2 +3*x +2*x -6
=x^2 * (x-3) * (x-2) - x*(x-3) +2 *(x-3)
= x^2 * (x-3) * (x-2) - (x-3) * ( x-2)
= (x-3) * (x-2) * (x^2 -1 )
= (x-3) * (x-2) * (x-1) * (x+1)
NOTE: * stands for multiplication.
Cheers.
2007-02-28 11:46:52 · answer #1 · answered by Dalilur R 3 · 1⤊ 0⤋
Try some easy guesses and see what you get.
I would automatically try x=1 and x=-1 which equate the formula to zero. So (x-1) and (x+1) must be factors.
This simplifies the formula to (x-1)(x+1)(x^2-5x+6)
and simplifying further (x-1)(x+1)(x-2)(x-3)
2007-02-28 11:48:42 · answer #2 · answered by kinvadave 5 · 0⤊ 0⤋
(x - 2)(x - 3)(x^2 - 1) = (x - 2)(x - 3)(x - 1)(x + 1)
2007-02-28 11:46:40 · answer #3 · answered by physicist 4 · 1⤊ 0⤋
Divide by (x - 1) and you will get the other factors.
2007-02-28 11:39:02 · answer #4 · answered by Runa 7 · 0⤊ 0⤋
(x-3) and (x+1) are factors
x^2-2x-3)x^4-5x^3+5x^2+5x-6(x^2-3x+2
x^4-2x^3-3x^2
-3x^3+8x^2+5x
-3x^3+6x^2+9x
2x^2-4x-6
2x^2-4x-6
thefactors are (x-3)(x+1)(x-2)(x-1)
2007-02-28 11:38:50 · answer #5 · answered by raj 7 · 2⤊ 1⤋