Question

use rational zeros theorem to find all the real zeros in the polynomial function. use zeros to factor f over real numbers.

f(x)=x^3+10x^2-13x-22
find real zeros of f?
use real zeros to factor f?

Answer 1

I suggest you start by using the rational roots theorem to find at least one root. You will learn more by making the effort yourself.

Answer 2

If I understood it I would not have to ask for help! I got it wrong in the 1st place and wanted to see the right answer. Thank you!!

Answer 3

The theorem says that if there is a rational root, it is (in this case) a factor of 22, which are one or more ofthese:
+/1, +/-2, +/-11 or +/-22.

See if any of those work.

Answer 4

thank you!

Answer 5

x = 2 is a solution and (x-2) is a factor.

The other factor is
(x^3+10x^2-13x-22)/(x-2)

Polynomial long division will reduce that to a quadratic.

Answer 6

6x^3+25x^2-24x+5