Warm-up - Home Page - mrsneubert.com · Warm-up Factor each polynomial. 1. 4x2 – 6x 2. 15y3 + 20y...
Transcript of Warm-up - Home Page - mrsneubert.com · Warm-up Factor each polynomial. 1. 4x2 – 6x 2. 15y3 + 20y...
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