How do you determine whether x-1 is a factor of the polynomial x4−3x3+2x2−x+1?

1 Answer
Ratnaker Mehta
Jan 31, 2017

(x−1) is a factor of p(x).

Explanation:

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

p(x)=x4−3x3+2x2−x+1.

To determine whether (ax+b) is a factor of p(x), we check
p(−ba). 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

⇒(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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