1. Factor each of the following.
2. a. Factor 2x² +11x +15 using algebra tiles.

Answer:

b. Factor 2x² +11x +15 symbolically.

Answer:

c. Explain how the two methods are similar.

Answer:

1. Near the beginning of Lesson 5.3, a strategy for factoring trinomials of the form x² + bx + c was developed by exploring the product of the binomials (x + p) and (x + q).

a. Explain how the development of this factoring strategy is an example of working backwards to solve a problem.

Answer:

b. The product of (x + p)(x + q) can be written as x² +(p + q)x + pq.

i. An intermediate step in this multiplication is

x² + px + qx + pq = x² + (p + q)x + pq.

Explain why px + qx = (p + q)x.

Answer:

ii. Explain why the expression x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c when factoring a trinomial of the form x² + bx + c.

Answer: