Question

Factor x^3-5x^2-25x+125

Answer 1

5x(x^2-x-5+25)

Answer 2

- no - thats gives 5x^3

Answer 3

x+ 5 or x-5 might be a factor
find f(5) and see if it = 0

Answer 4

So (x+5)(x-5)(x-5)

Answer 5

What type of roots of those?

Answer 6

we can factor out x^2 between the first two terms, and we can factor out -25x between the third and the fourth term, so we get this:
\[\Large {x^3} - 5{x^2} - 25x + 125 = {x^2}\left( {x - 5} \right) - 25x\left( {x - 5} \right)\]

Answer 7

OOOH
- did you guess that??
(x-5) is a factor because f(5) = 0

Answer 8

No. I just did (x^2-25)(x-5)

Answer 9

well you are correct

Answer 10

What type of roots are those?

Answer 11

And thanks youu

Answer 12

oops... we can factor out 25 between the third and the fourth terms, not 25 x:
\[\Large {x^3} - 5{x^2} - 25x + 125 = {x^2}\left( {x - 5} \right) - 25\left( {x - 5} \right)\]

Answer 13

right

Answer 14

- you beat me too it!!

Answer 15

So would the roots be -5,-5,5 or -5,5,5?

Answer 16

the roots are 5 and -5
root 5 is a duplicate

Answer 17

Ok but since the polynomial is 3 there has to be 3 roots?

Answer 18

- correction - that was rubbish
the roots are 5 , 5 and -5

Answer 19

How?

Answer 20

yes -5 and 5 duplicity 2

Answer 21

factors are (x + 5)(x - 5)(x - 5)

the fist gives x = -5 and the other 2 give x = 5

Answer 22

Ohhh<3

Answer 23

Thanks! :)

Answer 24

no 3 roots - because there are 2 5's

Answer 25

the graph will look a bit like