Help Desk - Get Answers to Your Questions

  • Context: MHB 
  • Thread starter Thread starter Tstuvshu
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on constructing a sixth-degree polynomial with specific factors: (x - 1), (x + 1), and (x - 2), including repeated linear factors and a quadratic factor without real roots. Multiple valid polynomial forms exist, such as (x - 1)4(x - 2)(x + 1) or (x - 1)2(x - 2)2(x + 1)2, where the sum of the exponents equals six. Additionally, any non-zero constant can multiply the product of these factors, allowing for further variations.

PREREQUISITES
  • Understanding of polynomial functions and their degrees
  • Knowledge of linear factors and their multiplicities
  • Familiarity with quadratic equations and their properties
  • Basic algebraic manipulation skills
NEXT STEPS
  • Explore polynomial factorization techniques
  • Learn about the Fundamental Theorem of Algebra
  • Study the characteristics of quadratic factors with no real roots
  • Investigate the impact of constant multiplication on polynomial graphs
USEFUL FOR

Students studying algebra, mathematicians focusing on polynomial theory, and educators looking for examples of polynomial construction.

Tstuvshu
Messages
1
Reaction score
0
Need help please
 

Attachments

  • 9FF5AA8D-6343-430C-9780-528FCA5691C6.jpeg
    9FF5AA8D-6343-430C-9780-528FCA5691C6.jpeg
    14.2 KB · Views: 113
Physics news on Phys.org
Any product of (x - 1), (x + 1), (x - 2) and a constant, with some repeated linear factors, quadratic factor without any real roots, or irreducible cubic factor that has 1, -1 or 2 as its roots.
 
What kind of "help" do want? For one thing, there is no single answer. There are many polynomials that satisfy these conditions! The only factors must be (x- 1), (x+ 1), and (x- 2) but that is only three and for a sixth degree polynomial you need six so some factors must be repeated. That could be $(x- 1)^4(x- 2)(x+ 1)$ or $(x-1)^2(x- 2)^2(x+ 1)^2$ or any combination of exponents that add to six. Also, the product of factors can be multiplied by any non-zero constant.
 

Similar threads

MHB Linear combination of sine and cosine function
  • · Replies 3 ·
Replies
3
Views
2K
MHB Calc Solved! Get Quick Help With Your Calculus Q
  • · Replies 1 ·
Replies
1
Views
1K
MathHelpBoards.com merges with PF
  • · Replies 42 ·
2
Replies
42
Views
5K
MHB Using advanced calculus for finding values
  • · Replies 2 ·
Replies
2
Views
1K
MHB Solve Calculus Problem: Answers to d, e, f in Math Paper
  • · Replies 3 ·
Replies
3
Views
1K
MHB Finding Limit: Get Step-by-Step Help Here
  • · Replies 1 ·
Replies
1
Views
1K
MHB Another Limit, without L'hospital rule
  • · Replies 6 ·
Replies
6
Views
2K
MHB Question on velocity and acceleration
  • · Replies 5 ·
Replies
5
Views
2K
MHB Confused: Seeking Help on Problem Solution
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Solve Line Integral Question | Get Math Help from Physics Forums
  • · Replies 5 ·
Replies
5
Views
2K