Problem: If bbb and ccc are constants and
(x+2)(x+b)=x2+cx+6(x+2)(x+b)=x^{2}+c x+6 (x+2)(x+b)=x2+cx+6
then ccc is
Answer Choices:
A. −5-5−5
B. −3-3−3
C. −1-1−1
D. 333
E. 555
Solution:
We have
x2+(2+b)x+2b=x2+cx+6x^{2}+(2+b) x+2 b=x^{2}+c x+6 x2+(2+b)x+2b=x2+cx+6
so
c=2+b and 6=2bc=2+b \quad \text { and } \quad 6=2 b c=2+b and 6=2b
Thus b=3b=3b=3 and c=5c=5c=5.