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