The root x = 1 has multiplicity 3 for the function f(x)=x^4-x^3-3x^2+5x-2 . true or false?

Question

The root x = 1 has multiplicity 3 for the function  f(x)=x^4-x^3-3x^2+5x-2 . true or false?

anonymous · Answer

If the root x=1 has a multiplicity of 3, then the following must be a factor of the function:
$$(x-1)^3$$So, start by expanding that expression. Then, check if it is a factor of the function using long division. If you need more assistance let me know.

anonymous · Answer

how would i expand it ?

anonymous · Answer

To expand it, multiply out:
$$(x-1)(x-1)(x-1)$$You can use the FOIL method to multiply two of them together, than multiply by the last one.

anonymous · Answer

okay thanks !

anonymous · Answer

You're welcome, glad I could help.