factor completely

2
x -6x+9

x^2 - 6 x + 9 = (x - 3)^2

To factor the given quadratic expression completely, we need to find two binomial factors.

Step 1: Look for common factors (if any)
In this case, there are no common factors among the terms.

Step 2: Find two numbers that multiply to give the constant term (9) and add up to give the coefficient of the middle term (-6).
The constant term is 9, and the coefficient of the middle term is -6. We need to find two numbers that multiply to give 9 and add up to give -6. The numbers that satisfy this are -3 and -3.

Step 3: Rewrite the quadratic expression using the two numbers found in Step 2.
2x^2 - 6x + 9 can be rewritten as:
2x^2 - 3x - 3x + 9

Step 4: Group the terms.
Group the first two terms together and the last two terms together:
(2x^2 - 3x) + (-3x + 9)

Step 5: Factor out the common factors from each group.
From the first group, factor out x:
x(2x - 3)
From the second group, factor out -3:
-3(2x - 3)

Step 6: Combine the factored expressions.
The factored expression is the product of the factored groups:
(x - 3)(2x - 3)

Therefore, the completely factored form of the expression 2x^2 - 6x + 9 is (x - 3)(2x - 3).