Answer:
= 9(x - 1)(x - 3).
Explanation:
To factor 9x^2 - 36x + 27, we can start by factoring out the greatest common factor (GCF), which is 9:
9x^2 - 36x + 27 = 9(x^2 - 4x + 3)
Next, we need to factor the quadratic expression inside the parentheses, which can be done using the product-sum method or by recognizing that the expression is a quadratic trinomial of the form x^2 - bx + c. Since the coefficient of x^2 is 1, we can easily see that the two factors must have the form (x - ?)(x - ?), where the question marks represent the two missing numbers we need to find.
To find these numbers, we can look for two numbers that multiply to give 3 (the constant term) and add to give -4 (the coefficient of x). It's easy to see that these numbers are -1 and -3:
x^2 - 4x + 3 = (x - 1)(x - 3)
Therefore, we can write:
9x^2 - 36x + 27 = 9(x^2 - 4x + 3) = 9(x - 1)(x - 3)
So the factored form of the polynomial is 9(x - 1)(x - 3).