Math question

[cartera]

If x^2+3x+c=(x+a)(x+b), for all a, what is the value of c?

1. a=1
2. b=2


OA D

[Neo2000]

Given x^2+3x+c=(x+a)(x+b)

(x+a)(x+b) = X^2 + (a+b)X +ab

Comparing to the first equation we get
ab = c
and
(a+b)X = 3X which means that (a+b) = 3

From the options
1. If a =1 then b has to equal 2 and c = 2
2. If b = 3 then a has to equal 1 and c = 2

Thus it is possible to answer from either Option alone