Find the product.

1. (2x + 3)(3x – 7)

2. (x – 11)(x + 11)

= 6x2 – 5x – 21

= x2 – 121

= 5(2x + 5) Factor.3. 10x + 25

4. 28x2 + 35x

5. x3 + 2x2 + 4x + 8

= 7x(4x + 5)

= (x2 + 4) (x + 2)

6. x2 + 11x + 30

7. x2 – 4x – 32

= (x + 6) (x + 5)

= (x + 4) (x – 8)

More warm-up Solve the following equation

(USE Factoring)28. 12 0x x

29. 2 8 0x x

More Warm-upSimplify the fraction

114

98. 2

45

60.

6

3

253.

30

x

x

3 4

5 2

244.

6

x y

x y

Standard: MM1A3e

Simplifying rational expressions

A fraction whose numerator and denominator are nonzero polynomials

Standard: MM1A3e

When a rational expression’s numerator and denominator have no factors in common (other than 1).

Process: Factor, then cancel.

Standard: MM1A3e

1. Simplify a Rational Expression

18

60

2

3

x

x

3

10x

Reduce the numbers and subtract the exponents.

Where the larger one is, is

where the leftovers go.

Standard: MM1A3e

2. Simplify a Rational Expressionx x

x

2

2

6

3

Factor the top

x x

x

( )

6

3 2Cross out the common factor x.

( )x

x

6

3

Standard: MM1A3e

3. Simplify a Rational Expression3

4 2

x

x x Factor the bottom

3

4

x

x x( ) Cross out the

common factor x.

3

4( ) x

Standard: MM1A3e

4. Simplify a Rational Expression

5 10

15

2x x

x

Factor the top

5 1 2

15

x x

x

( )Cross out the common

factors of 5 and x.

( )1 2

3

x

Standard: MM1A3e

5. Simplify a Rational Expression

x

x

2 16

3 12

Factor the top and bottom

( )( )

( )

x x

x

4 4

3 4Cross out the common factor (x + 4)

( )x 4

3

Standard: MM1A3e

Recognize Opposite Factors

When you have opposite factors, you will have to factor out a negative so that you can cancel.

Standard: MM1A3e

6. Opposite Factors1

2 32

x

x x

Factor the bottom

( )

( )( )

1

3 1

x

x x

(1 – x) on the top and (x – 1) on the bottom are opposites. Factor out a negative so they will cancel.

( )

( )( )

x

x x

1

3 11

3( )xStandard: MM1A3e

Practice #7

2

3

9

x

x

1

3x Standard: MM1A3e

Practice #82 6

4

x

3

2

x

Standard: MM1A3e

Practice #9

2

5

10 5

x

x x

1

2 1x Standard: MM1A3e

Practice #103

3 2

4

2 8

x

x x

2

4

x

x Standard: MM1A3e

Practice #113 2

2

x x

x

1x Standard: MM1A3e

Practice #122 12

3

x x

x

( 4)x Standard: MM1A3e