What is the quotient of b3+4b2-3b+126/b+7? a. b² + 11b + 80 r276 b. b² − 11b + 38 r140 c. b² − 3b + 18 r252 d. b² − 3b + 18

Let's try the one answer with no remainder: (b² - 3b + 18)
If this is the answer, then, when multiplied by b+7, we should get 
b³+4b²-3b+126
(b+7) (b² - 3b + 18)                                         Distribute
= b³ - 3b² + 18b + 7b² - 21b + 126                  Collect like terms
= b³ + 4b²-3b + 126                 
This number perfectly matches the numerator in the first term! 

Therefore, the answer is D) b² − 3b + 18