Factor - 4x + 24 - 4x^2

- 4 (x + 3) (x - 2)

Step-by-step explanation:

Given

- 4x + 24 - 4x² ← rewrite in standard form, that is

- 4x² - 4x + 24 ← factor out - 4 from each term

= - 4 (x² + x - 6) ← factorise the quadratic

Consider the factors of the constant term ( - 6) which sum to give the coefficient of the x - term ( + 1)

The factors are + 3 and - 2, since

3 * - 2 = - 6 and 3 - 2 = + 1, hence

x² + x - 6 = (x + 3) (x - 2), and

4x² - 4x + 24 = - 4 (x + 3) (x - 2)