Answer:
(x + 2)(2x - 7)
Step-by-step explanation:
Given
2x² - 3x - 14
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 14 = - 28 and sum = - 3
The factors are - 7 and + 4
Use these factors to split the x- term
2x² + 4x - 7x - 14 ( factor the first/second and third/fourth terms )
= 2x(x + 2) - 7(x + 2) ← factor out (x + 2) from each term
= (x + 2)(2x - 7)
Thus
2x² - 3x - 14 = (x + 2)(2x - 7) ← in factored form
