Warm - UpFactor each of the following polynomials.

1. x2 + 7x + 10 2. x2 – 25

3. 3x2 + 18x + 15 4. 3x + 15

Unit 1: Rational Expressions

Lesson 1:

Factoring and Simplifying

NC Goal 1.03:

Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems

Performance Standards

TLW…

1. Factor polynomials.

2. Simplify rational expressions by factoring and canceling

like terms in the numerator and the denominator.

Essential Questions

1. What is a rational expression?

2. How do you factor to simplify a rational expression?

1.What is a rational expression?

A rational expression is a fraction that contains a polynomial in the numerator and the denominator.

Ex. x2 + 7x + 10 x2 – 25

2. How do you factor to simplify a rational expression?

1. Factor the numerator

2. Factor the denominator

3. Cancel*You can only cancel

through multiplication!

Example #1 Simplify

x2 + 7x + 10 x2 – 25

Example #2 Simplify

3x2 + 18x + 15 1. Factor out a GCF

3x + 15 2. Factor

3. Cancel

Example #3 Simplify

2x2 + 13x + 15 1. Multiply 1st and last term

8x + 12 2. Write the expression

without the coefficient of x2

and with the new last term

3. Factor

4. Put the coefficient back in

front of each x

5. Find any GCFs

6. Cancel

You Try

1. x2 - 6x + 8 2. 3x2 - 7x - 6

x2 - 3x – 4 x2 - 3x – 4

Work Time Answers

Closure

Pre-Test Connections:

#s