Lesson 8.8

Factoring Trinomials (Positive)

The ultimate number puzzle. Find two numbers that multiply to C and add to B.

Introduction

We are reversing FOIL for expressions like . We need to find the original parentheses that created this. Today, everything is positive.

Past Knowledge

Lesson 8.6 (FOIL). You know that the Last term comes from multiplying, and the Middle term comes from adding.

Today's Goal

Factor where everything is plus signs.

Future Success

This is the heart of Algebra. You will use this to solve Quadratic Equations (Unit 9).

Key Concepts

The "X" Method

For :

Find two numbers that...

Multiply to

C

(The Last Number)

Add to

B

(The Middle Number)

Worked Examples

Example 1: The Basics

Basic

Factor:

1

The Puzzle

Multiply to 15.

Add to 8.

2

List Factors of 15

  • 1 and 15 (Adds to 16)
  • 3 and 5 (Adds to 8) ← WINNER!

Answer

Example 2: Just Double Check

Intermediate

Factor:

1

The Puzzle

Multiply to 9.

Add to 6.

2

Find the Factors

1 and 9 (Add to 10)

3 and 3 (Add to 6) ← WINNER!

Answer

Or written as .

Example 3: GCF First

Advanced

Factor:

1

Check GCF

Before doing the X method, look deeper. Everything divides by 2!

2

Factor Inside

Multiply to 8. Add to 6.

Numbers: 2 and 4.

Answer

Common Pitfalls

Adding vs Multiplying

Students often get confused. Remember: multiply for the LAST number, add for the MIDDLE number.

Forgetting the GCF

Factoring as is technically correct multiplication, but incomplete. ALWAYS pull the GCF out first.

Real-Life Applications

Physics Trajectories:

  • The height of a ball is .
  • To find when it hits the ground (), we must factor this equation.
  • Solving for tells us how long the ball is in numbers air.

Practice Quiz

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