Factor by grouping: 8x^3 - 12x^2 + 6x - 9.
2007-07-27 09:52:27 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
8x^3 - 12x^2 + 6x - 9 can be written as
8x^3 - 12x^2 + 3(2x - 3)
= 4x^2 (2x - 3) + 3(2x - 3)
= (2x - 3) (4x^2 + 3)
2007-07-27 10:05:42 · answer #1 · answered by Swamy 7 · 0⤊ 0⤋
You can factor "by grouping" when you have an even number of terms, and the ratio between pairs of terms are the same. In this case we have a 4 term polynomial and the ratio between pairs of terms are the same:
(-12)/8 = (-9)/6 = -1.5
When this is true you can factor the polynomial by grouping. It is easier to show you how it is done than explain it.
8x^3 - 12x^2 + 6x - 9
4x^2(2x-3) + 3(2x-3)
(4x^2+3)(2x-3)
2007-07-27 10:09:27 · answer #2 · answered by heartsensei 4 · 0⤊ 0⤋
8x^3 - 12x^2 + 6x - 9
Group:
= (8x^3 - 12x^2) + (6x - 9)
Factor:
= 4x^2(2x - 3) + 3(2x - 3)
Take out a common (2x - 3) term:
= (2x - 3) (4x^2 + 3)
2007-07-27 10:06:11 · answer #3 · answered by whitesox09 7 · 0⤊ 0⤋
let's change it up
8x^3+6x-(12x^2+9)
2x(4x^2+3)-3(4x^+3)
hence...
(2x-3)(4x^2+3)
2007-07-27 10:06:56 · answer #4 · answered by Kenneth H 3 · 0⤊ 0⤋