SOLUTION: write the polynomial function f(x)= x^5+x^3+2x^2-12x+8 as the product of linear factors

Question 835252: write the polynomial function
f(x)= x^5+x^3+2x^2-12x+8
as the product of linear factors
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

is not a linear factor.
It is a quadratic polynomial, and can only be factored using imaginary numbers.

HOW DO WE GET THAT?
Noticing that ,
we realize that is a factor of .
Dividing, we find that

Since ,
must be a factor of .
Dividing, we find that
.
So and ,
which means that

At this point, either we may realize that is zero for ,
or we may realize that is divisible by .
In either case we divide and find that .
So, putting it all together,
.

Alternatively, we may realize that

and since ,
dividing both sides by we conclude that

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