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

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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