Express 3(x^2) - 12x + 5 in the form a(x - b)^2 - c.

Starting with a(x - b)^2 - c, if we expand the bracket we get:

a(x^2 - 2xb + b^2) -c

Since we need to end up with the coefficient on x^2 being 3 and in the expression above x^2 is only multiplied by a, this gives us that a=3.

Substituting a=3 into the expression and multiplying the bracket by this gives:

3x^2 - 6xb + 3b^2 - c

In a similar way to before, we need to end up with the coefficient on x being minus 12. This means we can use the above expression to create an equation that can solve for b. The equation is: -6xb = -12x. Dividing both sides by -6x therefore gives us that b=2.

Substituting b=2 into the second expression we used gives: 

3x^2 - 12x + 12 - c

To get to the expression that the question asks for, the final stage is to find the value of c. We know that the value of the constant is +5, and so we can use the above expression in same same method as before to get the equation 12 - c = 5. Subtracting 5 from both sides and adding c allows us to solve for c=7.

In summary, a=3, b=2, c=7.

Finally, we should check our answer by substituing these values into the expression a(x - b)^2 - c. Doing this gives 3(x^2) - 12x + 5 and hence we have successfully answered the question.