Question

Solve the equation
x^3-4x^2-x+4=0
and list all the solutions.

Answer 1

\[x^3-4x^2-x+4=0\]

Answer 2

what is the common factor in 2 first terms?

Answer 3

x

Answer 4

cant we take \(x^2\) as common factor?

Answer 5

I guess so

Answer 6

well start by factoring out \(x^2\) in 2 first term

Answer 7

\[x^2(x-4)\]

Answer 8

right

Answer 9

now note that \(-x+4=-(x-4)\) and u have
\[x^3-4x^2-x+4=x^2(x-4)-(x-4)\]
what to do next?

Answer 10

I don't know.

Answer 11

we can take \(x-4\) as common factor...

Answer 12

x-4(1)-(1)

Answer 13

(x-4)(x^2-1)=0
x-4=0 or x2-1=0
x=4 & x=1 & x=-1

Answer 14

Thanks