Factoring the quadratic equation y= x^2 -x + 1?

To factor the quadratic equation y = x^2 - x + 1, we need to find two numbers that multiply to 1 (the coefficient of the constant term) and add up to -1 (the coefficient of the x term).

The two numbers that satisfy these conditions are -1 and -1. Therefore, we can rewrite the equation as:

y = x^2 - x - x + 1
y = x(x - 1) - 1(x - 1)
y = (x - 1)(x - 1)

Therefore, the factored form of the quadratic equation y = x^2 - x + 1 is y = (x - 1)^2.

y = x^2 - x - 1

Step 1: Find two numbers that add up to -1 and multiply to -1:

-1 and 1

Step 2: Rewrite the middle term using the two numbers found in Step 1:

y = x^2 - x + 1 - 2

Step 3: Group the first two terms and the last two terms:

y = (x^2 - x) + (1 - 2)

Step 4: Factor out the greatest common factors from each group:

y = x(x - 1) - 1(x - 2)

Step 5: Combine like terms:

y = (x - 1)(x - 2)

Therefore, the factored form of the quadratic equation is:

y = (x - 1)(x - 2)