Answer:
(x - 4)(2x + 3)
Explanation:
Given
2x² - 5x - 12
Consider the factors of the product of the coefficient of the x² term and the constant which sum to give the coefficient of the x- term.
product = 2 × - 12 = - 24 and sum = - 5
The factors are - 8 and + 3
Use these factors to split the x- term
2x² - 8x + 3x - 12 ( factor the first/second and third/fourth terms )
= 2x(x - 4) + 3(x - 4) ← factor out (x - 4) from each term
= (x - 4)(2x + 3) ← in factored form
The factors are (x - 4) and (2x + 3)