How do you determine whether x-1 is a factor of the polynomial 2x^3+4x^2-5x-12x3+4x2−5x−1?

1 Answer
Ratnaker Mehta
Feb 15, 2017

(x-1)(x−1) is a factor of p(x)p(x).

Explanation:

Let us denote the poly. by p(x), so, p(x)=2x^3+4x^2-5x-1.p(x),so,p(x)=2x3+4x2−5x−1.

A very simple test to check whether (x-1)(x−1) is a factor of p(x) :p(x): is

(x-1)" is a factor of "p(x) iff" the sum of the co-effs. of "p(x)" is zero."(x−1) is a factor of p(x)⇔ the sum of the co-effs. of p(x) is zero.

Here, in our Example, the sum of co-effs. of

p(x)=2+4-5-1=0p(x)=2+4−5−1=0

Hence, (x-1)(x−1) is a factor of p(x)p(x).

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