Let's solve the quadratic equations provided:

Equation b) $x^2 - 17x + 72 = 0$

To factor this, we need two numbers that multiply to 72 and add to -17. These numbers are -9 and -8. Thus, the factored form is:

$(x - 9)(x - 8) = 0$

So, the solutions are:

$x = 9 \quad \text{or} \quad x = 8$

Equation c) $x^2 - 3x - 28 = 0$

We need two numbers that multiply to -28 and add to -3. These numbers are -7 and 4. Thus, the factored form is:

$(x - 7)(x + 4) = 0$

So, the solutions are:

$x = 7 \quad \text{or} \quad x = -4$

Equation d) $x^2 + x - 12 = 0$

We need two numbers that multiply to -12 and add to 1. These numbers are 4 and -3. Thus, the factored form is:

$(x + 4)(x - 3) = 0$

So, the solutions are:

$x = -4 \quad \text{or} \quad x = 3$

Would you like more details on any of these solutions or have any questions? Here are some related questions to explore further:

1. What is the process of factoring quadratics in general?
2. How can you verify the solutions of a quadratic equation?
3. What happens if a quadratic cannot be factored easily? How do you solve it then?
4. What are the different methods of solving quadratic equations apart from factoring?
5. How do you apply the quadratic formula to solve these equations?

Tip: Always check your factored solution by expanding it to see if you get back the original quadratic equation!