If (ax + 2)(bx + 7) = 15x^2 + cx + 14 for all x, and a + b = 8, what are the two possible values for c?
A3 and 5
B6 and 35
C10 and 21
D31 and 41
Answer & Solution
Correct answer: D. 31 and 41
Expand: abx^2 + 7ax + 2bx + 14 = abx^2 + (7a + 2b)x + 14. So ab = 15 and c = 7a + 2b. With a + b = 8, the pair (a,b) satisfying ab = 15 is {3,5}. If a=3, b=5: c = 21 + 10 = 31. If a=5, b=3: c = 35 + 6 = 41.
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