How do you determine whether x-1 is a factor of the polynomial #x^4-3x^3+2x^2-x+1#?

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Answer 1 · 2017-01-31T09:35:11

#(x-1)" is a factor of "p(x)#.

Let us denote the given polynomial by #p(x)#, so that,

#p(x)=x^4-3x^3+2x^2-x+1.#

To determine whether #(ax+b)# is a factor of #p(x)#, we check
#p(-b/a)#. If this is #0, (ax+b)# is a factor of #p(x).#

So, for #(x-1),# we have to check #p(1)#.

#p(1)=1-3+2-1+1=4-4=0#

#rArr (x-1)" is a factor of "p(x)#.

It will be clear from the above discussion that, to determine whether

#(x-1)# is a factor of a given poly., we have to simply check whether

the sum of the co-effs. is #0.#

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