How do you factor completely # P(x)= x^3-2x^2+x-2#?

1 Answer
Mar 4, 2018

Answer:

Factored over the real numbers: #(x-2)(x^2+1)#

Factored over the complex numbers: #(x-2)(x+i)(x-i)#

Explanation:

We can factor by grouping:

#x^3+x-2x^2-2=x(x^2+1)-2(x^2+1)=#

#=(x-2)(x^2+1)#

This is all we can factor over the real numbers, but if we include complex numbers, we can factor the remaining quadratic even further using the difference of squares rule:

#x^2+1=x^2-i^2=(x+i)(x-i)#

This gives the following complex factoring:

#(x-2)(x+i)(x-i)#