Warm-up Factor each polynomial. 1. 4x2 – 6x 2. 15y3 + 20y

3. n2 + 4n + 3 4. p2 – p – 42

Warm-up Factor each polynomial. 1. 4x2 – 6x 2. 15y3 + 20y

Common Factor: 2x

2x 2x

2x( 2x – 3)

Common Factor: 5y

5y 5y

5y( 3y2 + 4)

Warm-up Factor each polynomial. 3. n2 + 4n + 3 4. p2 – p – 42

3

4 1 3

(n + 1)(n + 3)

-42

-1 6 -7

(p + 6)(p – 7)

Review Simplifying & Multiplying Rational

Expressions Standards: 2.0, 12.0, 13.0 Objective: I will simplify and multiply rational expressions.

Example: Simplify the rational expression.

€

7x + 21x + 3

€

=

x + 3

€

=71

7x + 21 CF: 7

7(

7 7

x + 3) = 7

Example: Simplify the rational expression.

€

164t + 24

€

=16

€

=4

t + 6

4t + 24 CF: 4

4(

4 4

t + 6) 1

4

€

=4x(x −2)

(x −2)(x −7)

€

4x2 −8xx2 −9x +14

€

=x2 −9x +14

14

-9 -2 -7

€

=4x

x −7

Example: Simplify the rational expression.

4x2 − 8x CF: 4x

4x(

4x 4x

x − 2)

€

=2x(x −6)

(x −1)(x −6)

€

2x2 −12xx2 −7x + 6

€

=x2 −7x + 6

6

-7 -1 -6

€

=2x

x −1

Example: Simplify the rational expression.

2x2 − 12x CF: 2x

2x(

2x 2x

x − 6)

€

=(x + 3)(x −9)

€

x2 −6x −27x2 + 5x + 6

€

=

x2 + 5x + 6

-27

-6 3 -9

€

=x −9x + 2

6

5 2 3

Example: Simplify the rational expression.

(x + 3)(x – 9)

(x + 2)(x + 3)

€

=2(x + 3)(x −3)

3 − x

€

2x2 −183 − x

€

=

3 − x

€

= −2(x + 3)

€

=

3 − x

Example: Simplify the rational expression.

2x2 – 18 CF: 2

2(

2 2

x2 – 9)

€

9

€

x2

2(x + 3)(x – 3)

= 3 = x

€

=2(x + 3)(x −3)

(−1)(x −3)

€

(2x +1)(2x −1)

€

6x

€

2x +13

⋅6x

4x2 −1

€

=2x +1

3⋅

€

=2x

1

1

Example: Multiply.

€

4x2

€

1

= 2x

= 1 2

€

2x −1

€

5x2

x −5⋅

x2 −10x + 25x −5

Example: Multiply.

€

x −5

25

-10 -5 -5

(x – 5)(x – 5)

€

5x2

x −5⋅

€

= 5x2

€

=(x + 9)(x −9)

⋅

€

x + 9

€

3x2

x −8

€

x + 9x2 −81

⋅3x2

x −8

€

=3x2

(x −9)(x −8)

Example: Multiply.

€

x2

€

81

= x

= 9

€

x + 410x2

€

x −2

⋅

€

x −22x −4

⋅x + 410x2

Example: Multiply.

2x – 4 CF: 2

2 2

2( x – 2)

€

=x + 420x2

€

6x2

€

3

⋅

€

10x −403

⋅6x2

12x3 −48x2

Example: Multiply.

10x – 40 CF: 10

10 10

10( x – 4)

12x3 – 48x2 CF: 12x2

12x2 12x2

12x2( x – 4) 1

2 5

1

€

=53