How do you write $P(x) = x^4 + 6x^3 + 7x^2 − 6x − 8$ in factored form?

Question

4258 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-18T10:37:12

(x+1)(x−1)(x+2)(x+4)

First thing to always remember is a bi quadratic has 4 roots whether they are distinct or not.

Start of with the basic

$+- 1$

We find that

$p(1),p(-1) = 0$
$=> (x-1)(x+1)$ are factors of $p(x)$

Lets divide

${p(x)}/{(x-1)(x+1)}$ = $x^2+6x+8$

$=> (x-1)(x+1)(x^2+6x+8) = p(x)$

Now factor $x^2+6x+8$

$=(x+2)(x+4)$

Now
$=> (x-1)(x+1)(x+2)(x+4) = p(x)$

We have found the four roots and hence we can be certain we have factored the given polynomial completely