Answer:
Correct answer: (2 x - 1) (x + 2)
Step-by-step explanation:
Given:
2 x² + 3 x - 2 = ( ) · ( )
2 x² + 3 x - 2 = 2 · ( x² + (3/2) x - 1) = 2 ( x² + 2 · x · (3/4) + (3/4)² - (3/4)² - 1)
2 x² + 3 x - 2 = 2 · ( (x + (3/4))² - (9/16) - 1) = 2 · ((x + (3/4))² - (9/16) - (16/16))
2 x² + 3 x - 2 = 2 · ((x + (3/4))² - (25/16)) = 2 · ((x + (3/4))² - (5/4)²)
2 x² + 3 x - 2 = 2 · (x + (3/4) - (5/4)) · (x + (3/4) + (5/4)) =
2 · (x - (2/4)) (x + (8/4))
2 x² + 3 x - 2 = 2 · (x - (1/2)) (x + 2) = (2 x - 1) · (x + 2)
2 x² + 3 x - 2 = (2 x - 1) · (x + 2)
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