Answer:
y = 2(x - 4)(x + 2)
Explanation:
given
y = 2x² - 4x - 16 ← factor out 2 from each term
y = 2(x² - 2x - 8) ← factorise the quadratic
consider the factors of the constant term (- 8) which sum to give the coefficient of the x- term (- 2)
the factors are - 4 and + 2 , since
- 4 × + 2 = - 8 and - 4 + 2 = - 2
use these factors to split the x- term
x² - 4x + 2x - 8 ( factor the first/second and third/fourth terms )
= x(x - 4) + 2(x - 4) ← factor out (x - 4) from each term
= (x - 4)(x + 2) ← in factored form
Then
y = 2x² - 4x - 16
y = 2(x - 4)(x + 2) ← in factored form