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
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