Originally Posted by
mcruz65 Find all integers b for which a2 + ba – 50 can be factored.
Factors of – 50 = (- 50, 1), (50 – 1), (- 25, 1), (25, 1), (- 10, 1), (10, -1), (- 5,1), (5,-1), (-2,1),(2,-1)
(a – 50)(a + 1) = a2 – 50a + a – 50 = a2 – 49a – 50
(a + 50)(a – 1 ) = a2 + 50a - a + 50 = a2 + 49a – 50
(a – 25)(a + 1) = a2 + a - 25a – 25 = a2 – 24a – 25
(a + 25)(a - 1) = a2 - a + 25a – 25 = a2 + 24a – 25
(a – 10)(a + 1) = a2 + a - 10a – 10 = a2 – 9a – 10
(a + 10)(a - 1) = a2 - a + 10a – 10 = a2 + 9a – 10
(a – 5)(a + 1) = a2 + a - 5a – 5 = a2 – 4a – 5
(a + 5)(a - 1) = a2 - a + 5a – 5 = a2 + 4a – 5
(a – 2)(a + 1) = a2 + a - 2a – 2 = a2 – a – 2
(a + 2)(a - 1) = a2 - a + 2a – 2 = a2 + a – 2