How do you list all possible roots and find all factors and zeroes of #x^4-x^3+14x^2-16x-32#?

1 Answer
Jul 5, 2018

Answer:

Please see the explanation below

Explanation:

The function is

#P(x)=x^4-x^3+14x^2-16x-32#

#=x^4-x^3-color(red)(2x^2)+14x^2+color(red)(2x^2)-16x-32#

#=(x^4-x^3-2x^2)+(16x^2-16x-32)#

#=x^2(x^2-x-2)+16(x^2-x-2)#

#=(x^2+16)(x^2-x-2)#

#=(x^2+16)(x+1)(x-2)#

The real roots are #(x=-1)# and #(x=2)# and the imaginary roots are #(x=4i)# and #(x=-4i)#

graph{x^4-x^3+14x^2-16x-32 [-36.53, 36.53, -18.27, 18.28]}