factorise c^2-8c+15

c^2 - 8c + 15 = ( c -3)(x-5)

You
can calculate the roots using the following formula:

x= [ -b
+-sqrt(b^2 - 4ac)]/2a

a = 1    b= -8    c =
15

==? x1= [ 8 + sqrt(64-4*1*15) ]/
2

          = [ 8 + sqrt(4)]/2 = (8+2)/2 =
5

==> x1= 5

==> x2= (
8-2)/2 = 6/2 = 3

==> x2= 3

We
know that if x1 and x2 are roots for f(x) then ( x-x1) and (x-x2) are factors of
f(x):

==> (x-5) and (x-3) are
factors.

==> ( c^2 - 8c + 15 = (
c-5)(c-3)