How do I factor x^4-12x^3+48x^2-64x?

Answer 1

factor out x : x(x^3 - 12^x2 + 48x -64)
since all the coeff are factos of 4 , trying x =4 , it is a soln

therefore x (x-4)(x^2 - 8x +16)
x^2 - 8x +16 = (x-4)^2

so the factorization is x(x-4)^3
solns for f(x) = 0 are x=0,4

Answer 2

Please don't post the same question multiple times.
The answer is to have a little patience for someone to show you how to do your problem [or well ... most seem keen on trying to show off and give away the entire answer lol]; reload the page [and make sure your browser settings are set to go out and get a new copy of the page each visit ]

also try to break any problem down step by step ... it will make life easier so in the above factor out an x and then look at the part you still dont have resolved

x^3 - 12x^2 + 48x - 64 and in order to get a cube you will have to have x^2 * x so set up your next step then figure out how to get it right
that is to say (x + ??) * (x^2 + ??x + ??) = x^3 - 12x^2 +48x - 64
if you have to at first ..... at least trial and error will help you learn ..then u will start to see how to speed it up

peace,
x

Answer 3

Start by factoring any common factors.
All terms have an x, so factor out an x
x^4 - 12x^3 + 48x^2 - 64x
= x(x^3 - 12x^2 + 48x - 64)

Answer 4

First, factor out the common x:

x( x³ - 12x² + 48x - 64 )

Now, notice that the first and last terms in the parentheses are perfect cubes. (64 = 4³.) Remember that for any two numbers a and b,

(a - b)³ = a³ - 3a²b + 3ab² - b³

Since the middle two terms both have coefficients that are multiples of 3, it looks really likely that the expression in the parentheses is really just (x-4)³. Let's test:

(x - 4)³ = x³ - 3(x²)(4) + 3(x)(4²) - 4³
= x³ - 12x² + 48x - 64

Eureka! So our entire expression really just = x( x - 4 )³.

Hope that's clear enough. Good luck!

MESSAGE for xkey: the reason the questioner deleted the original version of the question was because there was a mistake in it. It said "solve" instead of "factor."

Answer 5

First, always look for a common factor among all terms. In this case, it's x.

x(x³ - 12x² + 48x -64)

Next, for polynomials with 4 or more terms, check to see if it can be factored by grouping (this one can't), or by binomial expansion (this one can). With four terms, check to see if it's a cube. (You'll note the 1 3 3 1 pattern of coeeficients on a cube.)

x(x³ - 12x² + 48x -64)
= x(x - 4)³

Answer 6

48x 2

Answer 7

x^4 - 12x^3 + 48x^2 - 64x
x(x - 4)^3

i used www.quickmath.com

Answer 8

x^4-12x^3+48x^2-64x
=x*(x^3-12x^2+48x-64)

But we know that (a-b)^3=a^3 - 3a^2*b + 3a*b^2 - b^3
so If we replace 'a' by x and 'b' by 4

we get
x^4-12x^3+48x^2-64x
=x*(x-4)^3

Answer 9

Try grouping and if that doesn't work, factor out x

Answer 10

just have a few beers then the factor will come apparent