how do you factor 500t^2+2000t-16000?

Answer 1

Divide everything by 500. Or factor out 500.
(t^2+4t+32)= (t+4)(t+8)

Answer 2

First, factor out the greatest common factor, starting with variables. They don't all have a t, so move on to constants. The greatest common factor between 500, 2000, and 16000 is 500. Factor it out:

500t² + 2000t - 16000
= 500(t² + 4t - 32)

Now, factor the quadratic you got there:

t² + 4t - 32 = (t-4)(t+8)

Now, stick it back in the equation:

f(x) = 500 ( t-4 )( t+8 )

Answer 3

Solve using quadratic formula:
http://www.purplemath.com/modules/quadform.htm

or

Find 2 numbers that multiply to give you -8000000 and add up to give you 2000 and those are -2000 and 4000.
Then you change the equation around to factor:
500t^2 -2000t + 4000t -16000
(500t^2 -2000t) + (4000t -16000)
500t(t -4)+ 4000(t -4)
(500t+4000)(t-4)
500(t+8)(t-4)
500(t+8)(t-4) = 0 the 500 cancels
t+8=0 and t-4=0
t=-8 and t=4

Answer 4

500t^2+2000t-16000
500(t^2+4t-32)
500(t-4)(t+8)
so t=4 or -8

Answer 5

First factor out the largest coefficient
500, 2000 and 16,000 are all divisible by 500

500 t^2 + 2,000 t - 16,000
500(t^2 + 4t - 32)
500[(t-4)(t+8)]

Answer 6

500t^2+2000t-16000

Divide thru by 100

5t²+20t-160

Now divide thru by 5

t² + 4t - 32

(t + 8)(t - 4)
.

Answer 7

500(t^2+4t-32)
500(t+8)(t-4)

Answer 8

500 * (t^2+4t -32)

Answer 9

500t(t+4)-16000