Question

Pleeeeeeeease Help ME Examine the following function.

f(x)=2x^2−24x+54
What are the factors of the function?

2(x−3)(x+9)

2(x−6)(x−9)

2(x−3)(x−9)

(x−3)(x−9)

Answer 1

2(x - 3)(x - 9)

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