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12x² - 5x + 2 - 5 + 5 ≡ (ax + b)(3x - 2) + 5
(12x² - 5x - 3) + 5 ≡ (ax + b)(3x - 2) + 5
((12x² - 5x - 3)/(3x - 2))(3x - 2) + 5 ≡ (ax + b)(3x - 2) + 5
(4x + 1 - (1/(3x - 2)))(3x - 2) + 5 ≡ (ax + b)(3x - 2) + 5
a = 4
b = 1 - 1/(3x - 2)
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-x² + 9x - 3 ≡ (x + 1)(ax + b) + 5
-x² + 9x - 3 - 5 + 5 ≡ (x + 1)(ax + b) + 5
-x² + 9x - 8 + 5 ≡ (x + 1)(ax + b) + 5
(x + 1)(-x² + 9x - 8)/(x + 1) + 5 ≡ (x + 1)(ax + b) + 5
(x + 1)(-x + 10 - 18/(x + 1)) + 5 ≡ (x + 1)(ax + b) + 5
a = -1
b = 10 - 18/(x + 1)