Part 1: Which part of the quadratic formula tells you whether the quadratic equation can be solved by factorization or not?

The answer to Part 1 is the discriminant, b² - 4ac.

• If the discriminant is negative, the roots are complex numbers. You could solve by quadratic formula .
• If the discriminant is 0, the roots are -b/2a and -b/2a (repeated roots). You could solve by factoring.
• If the discriminant is positive, and a perfect square, you can solve by factoring.
Part 2: Consider the quadratic x² - 4x - 5. The discriminant is b² - 4ac = (-4)² - 4(1)(-5) = 16 + 20 = 36, which is a perfect square. Hence the quadratic factors are (x - 5)(x + 1). The roots are 5 and -1.

Last but not least, it is most important for a student to be able to memorize the quadratic formula.