2. Solve each equation by rewriting it in factored form and using the zero prod
   property. Show your reasoning.
   a.
   b.
   c.
   d.
   e.

To solve these equations, let’s rewrite them in factored form and apply the zero product property.

a.
First, we need to factor the quadratic. We look for two numbers that multiply to and add to . Those numbers are and . Thus, we can factor this as:

Using the zero product property, we set each factor equal to zero:


So, the solutions are and .

b.
First, move to the left side:

Next, we factor the quadratic: we need two numbers that multiply to and add to , which are and . So we have:

Setting each factor equal to zero gives us:


Thus, the solutions are and .

c.
To factor this quadratic, we look for two numbers that multiply to and add to . The numbers are and :

Setting each factor to zero results in:


So the solutions are and .

d.
We can rearrange this to . Next, we can rewrite it in factored form:

Setting each factor to zero gives us:


Thus, the solutions are and .

e.
First, we set this up as . To make it simpler, let’s expand it:

which simplifies to:

Now, we factor this quadratic. We need numbers that multiply to and add to , which are and :

Therefore, setting both factors to zero, we find:


The solutions are and .