# Lesson 8 The Wow Factor Solidify Understanding

## Learning Focus

Use diagrams to factor trinomial expressions when the leading coefficient is not

How can we factor

## Open Up the Math: Launch, Explore, Discuss

Optima’s Quilts sometimes gets orders for blocks that are multiples of a given block. For instance, Optima got an order for a block that was exactly twice as big as the rectangular block that has a side that is

### 1.

An open area model of this block is shown here along with the two equivalent expressions for area. What do you notice? What do you wonder?

### 2.

Try using some of the observations to factor each of the following expressions:

#### a.

#### b.

#### c.

#### d.

Because she is a great business manager, Optima offers her customers lots of options. One option is to have rectangles that have side lengths that are more than one

### 3.

What do you notice about the diagram and the equation for area? What do you wonder?

### 4.

Use your observations to complete the diagram. Be sure to fill in the lengths of the side and the missing areas.

Try a few on your own.

### 5.

### 6.

### 7.

As she is working on the orders, one of the employees, Anushka, stops and says, “Hey, wait! I noticed on problem 5 that if I multiply the coefficients of the first and last term, I get

On problem 6, when I multiply

### 8.

Does the pattern work for problem 7? Explain why or why not.

### 9.

If you think the pattern that Anushka noticed will help, try it to write

### 10.

There’s one more twist on the kind of blocks that Optima makes. These are the trickiest of all, because they may have more than one

Here’s an example: Complete the diagram using the sides that are given, and write the two expressions for area.

### 11.

Anushka has partially completed this diagram for you. The area of the block is:

### 12.

All right, let’s put it all together for some tricky ones! They may take a little messing around to get the factored expression to match the given expression. Check your answers to be sure that you’ve got them right. Factor each of the following.

#### a.

#### b.

#### c.

#### d.

## Ready for More?

Challenge your partner by making your own trinomial expressions to factor. You’ll need to start with the factored form, multiply it out, and exchange it with your partner without the answers. Your partner will work the one that you wrote, and you will work the one they wrote. When you’re done, check your work and see who has the wow factor!

## Takeaways

Factoring trinomials in the form

Example:

## Lesson Summary

In this lesson, we learned to factor trinomials in the form

For each given quadratic equation, state the vertex, the line of symmetry, the stretch, and whether the quadratic has a maximum or a minimum.

### 1.

Vertex:

Line of symmetry:

Stretch:

Maximum or Minimum:

### 2.

Vertex:

Line of symmetry:

Stretch:

Maximum or Minimum:

Given the