Answer:
(x - 4)
Step-by-step explanation:
Given
(2x - 5)² + 3(2x - 5) - 18 ← expand (2x - 5)² using FOIL
= 4x² - 20x + 25 + 6x - 15 - 18 ← collect like terms
= 4x² - 14x - 8 ← factor out 2 from each term
= 2(2x² - 7x - 4) ← factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 4 = - 8 and sum = - 7
The factors are - 8 and + 1
Use these factors to split the x- term
2x² - 8x + x - 4 ( factor the first/second and third/fourth terms )
= 2x(x - 4) + 1(x - 4) ← factor out (x - 4) from each term
= (x - 4)(2x + 1)
Thus
(2x - 5)² + 3(2x - 5) - 18
= 2(x - 4)(2x + 1)
with (x - 4) as one of the factors
