Which polynomial cannot be factored?

A  c^2 - 3c - 10

This one can be factored because we can think of two integers 5 and 2
which have product 10 and DIFFERENCE (since the last sign is MINUS) 3,
the absolute value of the middle coefficient -3.

It factors as (c-5)(c+2) The signs are DIFFERENT and the larger, 5,
gets the sign of the middle term -3 

B  x^2 - 11x + 10

This one can be factored because we can think of two integers 10 and 1
which have product 10 and SUM (since the last sign is PLUS) 11,
the absolute value of the middle coefficient -11.

It factors as (x-10)(x-1) The signs are THE SAME and they BOTH
get the sign of the middle coefficient -11 

C  b^2 - b - 12

Think of it as

   b^2 - 1b - 12

This one can be factored because we can think of two integers 4 and 3
which have product 12 and DIFFERENCE (since the last sign is MINUS) 1,
the absolute value of the middle coefficient -1.

It factors as (b-4)(b+3). The signs are DIFFERENT and the larger, 4,
gets the sign of the middle term -1


D  y^2 - 9y + 15

This one cannot be factored because we cannot think of any two 
integers which have product 15 and SUM (since the last sign is PLUS) 9,
the absolute value of the middle coefficient -9.

E  2x^2 + 5x + 3 

This one can be factored but it is requires a different method
from the others since the coefficient of the squared term is not 1.

But it factors by trial and error or the AC method as 

(x+1)(2x+3)

Edwin