Answer :

Given, p(X) = x2 – 2x + 1


Now, we need to write the given polynomial as a product of first degree polynomial and p(x) = 0


x2 – 2x + 1 = 0


The given equation can be written as follows


(x – 1)(x – 1) = 0


Since, we know that x2 – 2x + 1 can be written as (x – a)(x – b)


x2 – 2x + 1 = x2 – (a + b)x + ab


coefficient on either side of the polynomial is same and a + b = 2 and ab = 1


we must find two numbers that satisfy a + b and ab we get, 1 and 1 as the numbers


(x – 1)(x – 1) are the product of first degree polynomial


p(x) is 0 if (x – 1) is 0


x – 1 = 0


x2 – 2x + 1 = 12 – 2(1) + 1 = 1 – 2 + 1 = 0


Hence, (x – 1)(x – 1) are the first degree factors of the polynomial and 1 is the solution of the given polynomial x2 – 2x + 1


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