Search 74,320 tutors
0 0

# can you please factor out -12x^5+4x^4+4x^2

I need it as fast as possible

Hi Bryce;
I have been working on this.  Are you sure you copied this exactly right?
I think the expression should have been degree 6, not 5;
i.e., f(x) = –12x^6 + 4x^4 + 4x^2.
Thank you!
"I need it as fast as possible"

Why?

If the problem were to factor g(x) = –15x^6 + 5x^4 + 3x^2:

g(x) = –15x^6 + 6x^4 + 3x^2

g(x) = –3x^2(5x^4 – 2x^2 – 1)

h(x) = 5x^4 – 2x^2 – 1

h(x) = 5(x^2)^2 – 2(x^2) – 1

x^2 = (- -2 ± √(4-4(-5)) )/(2*5)

x^2 = (2 ± 2√(1+5) )/(2*5)

x^2 = (1 ± √(6) )/5

x = ± √( (1 ± √(6) )/5 )

g(x) = –3x^2(x ± √( (1 ± √(6) )/5 ) )

g(x) =
–3x^2
* (x – √( (1 + √(6) )/5 ) )
* (x + √( (1 + √(6) )/5 ) )
* (x – √( (1 – √(6) )/5 ) )
* (x + √( (1 – √(6) )/5 ) )
notice that what each term has in common is a factor of 4x2

so you get 4x2(-3x3 + x2 + 1)

you can check it by distributing the 4x2 back into the (-3x3 + x2 + 1)

another way of looking at it, if it helps, is once you realize that each term has a 4x2 as a factor, then you divide each term by 4x2 which is how you then get the other factor of (-3x3 + x2 + 1)