Download presentation

1
**6.2 Polynomials and Linear Factors**

At the end of this lesson, you should be able to: Factor sums and differences of cubes Solve a polynomial equation by factoring Write a polynomial function from its zeros

2
**Factoring the Sums and Differences of Cubes**

13 = _ 23 = _ 33 = _ 43 = _ 53 = _ 63 = _ 73 = _ 83 = _ 93 = _ 103 = _ 1 8 27 64 125 216 343 512 729 1000 Being familiar with perfect cubes will make cubing binomials and factoring sums and differences of cubes easier.

3
**Special Factoring Patterns**

…more know-by-♥ stuff! Special Factoring Patterns Sum of Two Cubes u3 + v3 = Example: u = Difference of Two Cubes u3 - v3 = u = (u + v) (u2 - uv + v2) (u - v) (u2 + uv + v2)

4
**Factor the polynomials:**

a. x3 - 27 b. x3 - 64 c. x d. x e. 4x f. 3x

5
**REVIEW: FACTORING BY GROUPING**

Factor the polynomials: a. 4x3 - 6x2 + 10x – 15 b. x3 - 2x2 - 4x + 8

6
**REVIEW: Factoring By Using Combined Methods**

Factor the polynomial COMPLETELY: 2x x2 + 12X

7
**ZERO PRODUCT PROPERTY Recall: Let a and b be real numbers.**

If ab = 0, then a = 0 or b = 0. Alert! This property connects factoring to solving equations!

8
**SOLVING POLYNOMIAL EQUATIONS BY FACTORING**

Solve the following equations by factoring: a. 3x4 = 48x2 b. x c. 5x

9
FACTOR THEOREM You can reverse the process and write the linear factors when you know the zeros (solutions). The relationship between the linear factors of a polynomial and the zeros of a polynomial is given by the Factor Theorem. The expression x – a is a linear factor of a polynomial if and only if the value a is a zero of the polynomial function. Write the factors of a polynomial whose zeros are 2, 2, & -3.

10
**WRITING A POLYNOMIAL FUNCTION FROM ITS ZEROS**

Alert! A repeated zero is called a multiple zero. A multiple zero has a multiplicity equal to the number of times the zero occurs. What is the multiplicity of the polynomial function? Explain.

11
**Final Checks for Understanding**

Given x3 - 4x2 = - 4x, determine the following: Factors: __________________ Solutions: X-intercepts: Zeros:

12
Homework Connections: Zeros, Factors, and Solutions WS, plus text_______________

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google