What is the factored form of 3c²+24c+48?

1st step factor 3 out of each number in the equation to get:

3 (c^2+8c+16)

16 can be rewritten as 4^2 to get:

3 (c^2+8c+4^2)

4+4 = 8 (the middle number)

so the factor would be 3 (c+4) ^2