Answer:
2(x - 3)(x - 9)
Step-by-step explanation:
Given
f(x) = 2x² - 24x + 54 ← factor out 2 from each term
= 2(x² - 12x + 27) ← factor the quadratic
Consider the factors of the constant term (+ 27) which sum to give the coefficient of the x- term (- 12)
The factors are - 3 and - 9 , since
- 3 × - 9 = + 27 and - 3 - 9 = - 12 , thus
x² - 12x + 27 = (x - 3)(x - 9) and
f(x) = 2(x - 3)(x - 9) ← in factored form
