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(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

1/3 + 1/5 = 8/15.

step-by-step explanation:

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