If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2
Please explain your answer. Thanks
Here, x^2 +3x +c=(x+a)(x+c)
or, x^2 +3x +c =x^2+x(a+b)+ab
Now you can tell 3x = x(a+b), so c=ab
From statement 1, you never get the value of b. so it is insufficient.
From statement 2, you never get the value of a. so it is insufficient.
From the both statements you get the value of both a &b. so it is sufficient. a=1 & b=2 and ab=2
Again your taken condition 3x= x(a+b) is also fulfilled. just like 3x= x(1+2).