Factor this with explanation: -4x^4 + 8x^3 - 16x^2 + 32x
2007-02-05 15:31:14 · 3 answers · asked by 511@ 4 in Science & Mathematics ➔ Mathematics
Facto out the obvious 4x:
-4x(x^3 - 2x^2 + 4x - 8)
Now notice that for x = 2 this is 8 - 8 + 8 - 8 = 0, so x - 2 is a factor:
-4x(x - 2)(x^2 + 4)
So this is as far as it can go for reals, for complex numbers
-4x(x - 2)(x - 2i)(x + 2i)
2007-02-05 15:39:26 · answer #1 · answered by sofarsogood 5 · 1⤊ 0⤋
Factoring is based on what all the represented have in common.
What do they all have in common? 4x. Divide everything by 4x and type the results inside the parenthesis:
4x*(-x^3+2x^2-4x+8)
2007-02-05 23:34:58 · answer #2 · answered by F B 3 · 0⤊ 1⤋
using grouping
(-4x^4+8x^3)(-16x^2+32x)
factor our -4x^3 on the left and -16x on the right because it is the common term...so...
-4x^3(x-2)-16x(x-2)
since (x-2) is like terms, we count them as one..so...
-4x^3-16x(x-2)
wait we're not done!! -4x^3-16x can still be factored further...so...
-4x(x^2-4) ---> waittt....still not done here (x^2-4) is factorable..so..
-4x(x+1)(x-1)
and now put it together with what we got before....and viola...
-4x(x+2)(x-2)(x-2)
= -4x(x+2)(x-2)^2
=D -->done and factored completely xD
2007-02-05 23:39:05 · answer #3 · answered by tonyma90 4 · 0⤊ 2⤋