how do you factor x^3-3x^2+2x-6?

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how do you factor x^3-3x^2+2x-6?

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2007-03-04 05:37:31 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

4 answers

x^3-3x^2+2x-6
x^2(x-3)+2(x-3)
=(x-3)(x^2+2)

2007-03-04 06:31:50 · answer #1 · answered by alpha 7 · 0⤊ 0⤋

The factors of x^3 are x, x, x.
The factors of 6 are 1,2,3 or 1,1,6

Notice that x^3-3x^2 is exactly x^2/2 times 2x-6.
So you can divide by x-3
(x^3-3x^2+2x-6)/x-3 = x^2+2
x^2+2 cannot be factored.

Answer is (x-3)(x^2+2)
x = 3
x = sqrt(-2) = i(sqrt2), -i(sqrt2)

2007-03-04 13:55:46 · answer #2 · answered by Steve A 7 · 0⤊ 0⤋

= x^2(x-3)+ 2 (x-3) =
(x-3)(x^2 +2)

2007-03-04 14:02:51 · answer #3 · answered by Sarah 2 · 0⤊ 0⤋

x^2 [x-3] + 2 [x-3] = 0

[x^2+2] [x-3]=0

x=3

2007-03-04 13:59:48 · answer #4 · answered by russiantoronto2003 2 · 0⤊ 0⤋