Explained: "How should I factor this polynomial: x3−x2−4x−6"

eszkortwxp

Answered question

2022-04-23

How should I factor this polynomial:

x^{3} - x^{2} - 4 x - 6

Jonas Dickerson

Beginner2022-04-24Added 22 answers

Typically when you have a polynomial of the form

f (x) = x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + \dots + a_{n}

where

a_{k} \in Z

, to factorize it, it is a good idea to first plug in the values of the divisors of

a_{n}

f (x)

with the hope that it will evaluate to 0. In your case, the polynomial is

f (x) = x^{3} - x^{2} - 4 x - 6

The divisors of -6 are

[\pm 1, \pm 2, \pm 3]

. We find that

f (\pm 1) \neq 0, f (\pm 2) \neq 0

and

f (- 3) \neq 0

, while

f (3) = 0

Hence we have

f (x) = (x - 3) (x^{2} + a x + b)

. We get that

- 3 b = - 6

and

a - 3 = - 1

. Hence, we get that

b = 2

and

a = 2

. Hence

f (x) = (x - 3) (x^{2} + 2 x + 2)

= (x - 3) ({(x + 1)}^{2} + 1) = (x - 3) (x + 1 - i) (x + 1 + i)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?