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3x² + 10x = 8 Rewrite as: 3x² + 10x - 8 = 0
The only way to get 3x² is 3x and x
(3x + -- ) (x + --)
The factors of 8 are {1 2 4 8} so the answers must be a pair of them.
With 4 factors, and a negative sign (the -8), there are only 8 ways this can be written:
(3x + 1)(x - 8) = 3x² - 23x - 8
(3x + 2)(x - 4) = 3x² -10x - 8 (almost)
(3x + 4 )(x - 2) = 3x² - 8x - 8
(3x + 8)(x - 1) = 3x² +5x - 8
(3x - 1)(x + 8) = 3x² +23x - 8
(3x - 2)(x + 4) = 3x² + 10x -8 ◄ Success!
(3x - 4)(x + 2) = 3x² +2x - 8
(3x - 8)(x + 1) = 3x² -5x - 8
Trial and error, error, error, is the key to this kind of problem. Seeing the -10x early can point you to see that maybe changing the signs can work. ■
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