Write each polynomial below as a product of first degree polynomials. Write also the solutions of the equation p(x) = 0 in each.

p(x) = x² – 2x + 1

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