How do you factor: r^3 - 6r^2 + 12r - 8?
I have been trying but i can't seem to get it to add up correctly. I got (r -1)(r -4)(r-2) but that is not correct.
Update:It needs to be factored in the form of ( x +- b)(x +- a)(x +- c).
I have been trying but i can't seem to get it to add up correctly. I got (r -1)(r -4)(r-2) but that is not correct.
Update:It needs to be factored in the form of ( x +- b)(x +- a)(x +- c).
Comments
r^3 - 6r^2 + 12r - 8
let x = 2
2|...1....-6....12....-8
............2.....-8.....8
--------------------------------
......1....-4.....4.......0
= (r - 2)(r^2 - 4r + 4)
= (r - 2)(r - 2)(r - 2)
= (r - 2)^3 answer//
Using rational root test, we find possible rational roots are:
±1, ±2, ±4, ±8
Trying these, we find that r = 2 is a root (so (râ2) is a factor)
Now we use synthetic division to find quadratic factor
2 . | . 1 .. â6 ... 12 .. â8
.... | ......... 2 .. â8 .... 8
.... --------------------------
........ 1 .. â4 .... 4 .... 0
r³ â6r² + 12r â 8
= (r â 2) (r² â 4r + 4)
= (r â 2) (r â 2) (r â 2)
= (r â 2)³
MαthmÏm
r³-6r²+12r-8
You can rewrite this as r³-3*2r²+3r(2)²-(2)³ and comparing this to
(a-b)³ = a³-3a²b + 3b²a - b³
you see that here a = r and b= 2, and
r³-6r²+12r-8 = r³-3*2r²+3r(2)²-(2)³ = (r-2)³
Or
Rearrange r³-6r²+12r-8
r³-8-6r²+12r
Factorize r³-8 as (r-2)(r²+2r+4) and -6r²+12r as -6r(r-2). So you have
(r-2)(r²+2r+4)-6r(r-2)
Factor out r-2
(r-2)(r²+2r+4-6r) = (r-2)(r²-4r+4)
And you can rewrite (r²-4r+4) as (r-2)²
So you have
(r-2)(r-2)² = (r-2)³
r^3-6r^2+12r-8=
(r^3-2^3)-6r(r-2)=
(r-2)(r^2+2r+4)-6r(r-2)=
(r-2)(r^2-4r+4)=
(r-2)(r-2)^2=
(r-2)^3
or use the formula:
r^3-3(r^2)(2)+3r(2^2)-2^3=
(r-2)^3
Angels answer is horrifyiny....Horrifyingly WRONG
Use Synthetic Division aand you wwill find that 2 works.
The Depressed equation is x$2 - 4x + 4
ANSWER.....( x - 2 ) ^ 3
r^3 - 2r^2 - 4r^2+ 12r - 8
r^2(r-2) - 4r(r-1)+ 8(r - 1)
r^2 (r-2) - 4(r-2) (r-1)
(r-2) [r^2 - 4(r-1)]
(r-2) (r-2) (r-2)
use sythetic division, the formula u ve used is for quadratic not cubic thats why the answers are wrong
answers should be
x=-0.52,3.26