Question

Factor the polynomial and find all (real and fake) its roots:
x^5-4x^3-x^2+4

Answer 1

f(1) = 1-4-1 + 4 = 0
so (x-1) is a factor
we can now divide by x-1
and se if the quotient can be factored

but because of the +4 at the end 2 or -2 may be factors:
f(2) = 32 - 32 - 4 + 4 = 0
f(-2) = = -32 + 32 - 4 + 4 = 0

so (x+2) and (x -2) are also factors

Answer 2

i have to go now - there are another 2 factors which could be complex (what u called fake?)

Answer 3

sorry - must go

Answer 4

Yes but go you know how you would divide those factors into the original equation. And yes, i call them fake, which they are imagery, or complex, which comes in pairs and are Complex Conjugates of each other.

Answer 5

This is easier than I thought. Let's try factoring by grouping:

x&5

Answer 6

(x^5-4x^3)-(x^2-4)
x^3(x^2-4)-1(x^2-4)
(x^3-1)(x^2-4)
(x-1)(x^2+x+1)(x-2)(x+2)
x=1,2,-2 and the complex roots of x^2+x+1

Answer 7

Use the quadratic formula to find the roots of x^2+x+1

Answer 8

ok i can do that