C. Factoring Trinomials by Decomposition

C. Factoring Trinomials by Decomposition

As you saw in Lesson 5.1, trinomials of the form can be produced by multiplying two binomials of the form . You also saw earlier in this Lesson that some trinomials of this form can be factored using algebra tiles. Can trinomials of the form also be factored symbolically?

Investigation

The following table shows pairs of binomials and their products, in the form .

1. 
   

1. Try to find a way to determine a using m, n, p, and q.
   [Hint: you won't need to use all four.]
   
   

2. Try to find a way to determine b using m, n, p, and q.
   
   

3. Try to find a way to determine c using m, n, p, and q.
   
   
   

2. If possible, use the relationships you determined in part 1 to factor .