Home
Add Document
Sign In
Register
Adding, Subtracting, and Multiplying Polynomials - Killingly Public
Home
Adding, Subtracting, and Multiplying Polynomials - Killingly Public
Adding, Subtracting, and. Multiplying Polynomials. Goals p Add, subtract, and multiply polynomials. p Use polynomial operations in real-life problems...
0 downloads
16 Views
59KB Size
DOWNLOAD
Recommend Documents
No documents
6.3
Adding, Subtracting, and Multiplying Polynomials Goals p Add, subtract, and multiply polynomials. p Use polynomial operations in real-life problems.
Your Notes
Example 1
a.
Adding Polynomials Vertically and Horizontally
2x3 3x2 7x 5 3x3 2x2 3x 5x 3 x 2 4x 5
b. (x3 6x 4) (6x3 2x2 9x 2) x 3 6x 3 2x2 6x 9x 4 2 5x 3 2x2 3x 2
Example 2
a.
Subtracting Polynomials Vertically and Horizontally
7x3 4x2 x 4
7x 3 4x2 x 4
(5x3 x2 x 6)
5x 3 x2 x 6 2x3 5x2 2x 2
b. (3x4 9x3 2) (2x4 6x3 2x 4) 3x4 9x3 2 2x 4 6x 3 2x 4 x 4 3x 3 2x 6
Example 3
Multiplying Polynomials Vertically
x2 x 3 x2 2x 2 2x 6
130
Multiply x2 ⴚ x ⴙ 3 by 2.
x 3 x 2 3x
Multiply x2 ⴚ x ⴙ 3 by x.
x3 x2 x 6
Combine like terms.
Algebra 2 Notetaking Guide • Chapter 6
Your Notes
Example 4
Multiplying Polynomials Horizontally
Multiply the polynomials. (x 2)(3x2 x 5) (x 2) 3x 2 (x 2) x (x 2) 5 3x 3 6x2 x2 2x 5x 10 3x 3 7x2 7x 10
Example 5
Multiplying Three Binomials
Multiply the polynomials. (x 2)(x 1)(x 3) ( x2 x 2 )(x 3) ( x2 x 2 )(x) ( x 2 x 2 )(3) x 3 x2 2x 3x2 3x 6 x 3 2x2 5x 6
SPECIAL PRODUCT PATTERNS Sum and Difference
Example
(a b)(a b) a2 b2
(x 3)(x 3) x2 9
Square of a Binomial (a b)2 a2 2ab b2
(y 4)2 y2 8y 16
(a b)2 a2 2ab b2
(3t 2 2)2 9t 4 12t 2 4
Cube of a Binomial (a b)3
(x 1)3
a3 3a2b 3ab2 b3 (a b)3
x3 3x2 3x 1 (p 2)3
a3 3a2b 3ab2 b3
p3 6p 2 12p 8
Lesson 6.3 • Algebra 2 Notetaking Guide
131
Your Notes
Example 6
Using Special Product Patterns
Multiply the polynomials. a. (3z 4)(3z 4) ( 3z )2 4
2
9z2 16 b. (4x2 3y)2 ( 4x2 )2 2( 4x2 )( 3y ) ( 3y )2 16x 4 24x2y 9y 2 c. (cd 4)3 ( cd )3 3( cd )2( 4 ) 3( cd )( 4 )2 4 c 3d 3 12c 2d 2 48cd 64
Checkpoint Complete the following exercises.
1. Add (3x2 3x 7) (x2 9x 5).
2x2 6x 2 2. Subtract (6x3 x2 1) (2x3 6x 3).
4x3 x2 6x 2 3. Multiply (x 3)(x 1)(x 7).
Homework
x3 5x2 17x 21 4. Multiply (2w 3)2.
4w2 12w 9
132
Algebra 2 Notetaking Guide • Chapter 6
3
×
Sign In
Email
Password
Remember me
Forgot password?
Sign In
Login with Facebook
Login with Google