Factorise p(x) as a product of linear factors

In summary: The Attempt at a SolutionIt's the solution, but i have a feeling that there is a more correct way of doing it. At least i need a way to write it so it is mathematical...
Physics news on Phys.org
  • #2
Last edited by a moderator:
  • #3
jbunniii said:
Can you start by stating the rational root theorem, and what it says about the possible rational roots of the polynomial?

ok! i will try that. :smile:
 
  • #4
After you find one root, I would use synthetic division to find the others.

But I guess it this case you really don't have to.
 
  • #6
The scan of your work is illegible. It appears that you did your work on graph paper, and possibly in pencil, making what you wrote very difficult to read.
 
  • #7
hostergaard said:
Here is it finished, could somebody prof-read it and comment? tell if there's some improvements to be done. ;-)
http://img33.imageshack.us/img33/72/opgave3.th.jpg

Guesswork is a good thing in mathematics, but guesswork often need some kind of reasoning. Drawing a graph by hand / on computer is not guesswork in this case. You should come up with a more sophisticated way of showing what your guesswork builds on.

One way to go by, is to look at the last number in the polynom, and factorize that number, finding numbers that constitute 56. You would then get some of the roots you have come up with doing your "guesswork". After that, do polynom division. Or two.
 
Last edited by a moderator:

1. What is factorising an expression?

Factorising an expression means breaking it down into smaller parts or factors that can be multiplied together to get the original expression.

2. What are linear factors?

Linear factors are expressions of the form (x-a), where x is a variable and a is a constant. They represent linear equations with a slope of 1.

3. Why is it important to factorise p(x) as a product of linear factors?

Factorising p(x) as a product of linear factors allows us to solve the equation by setting each factor equal to 0 and finding the roots of the equation. It also helps in simplifying complex expressions and identifying patterns.

4. How can I factorise p(x) as a product of linear factors?

To factorise p(x), you can use methods such as grouping, difference of squares, or the quadratic formula. It is important to first check for any common factors and then use these methods to break the expression down into linear factors.

5. Can all expressions be factorised into linear factors?

No, not all expressions can be factorised into linear factors. Some expressions may have factors that are not linear, such as quadratics or higher degree polynomials. In these cases, we can use other methods such as completing the square or using the rational roots theorem to find the factors.

Similar threads

Direct Proof that every zero of p(T) is an eigenvalue of T
    • Calculus and Beyond Homework Help
Replies
24
Views
797
Factoring a quartic polynomial
    • Calculus and Beyond Homework Help
Replies
12
Views
2K
Finding the minimum length of a median in a triangle
    • Calculus and Beyond Homework Help
Replies
31
Views
4K
Inner Product, Triangle and Cauchy Schwarz Inequalities
    • Calculus and Beyond Homework Help
Replies
5
Views
3K
Eigenvectors and orthogonal basis
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Solving a Second Order Non-Linear PDE with Undetermined Coefficients
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Derivative of two polynomials, one of them being squared
    • Calculus and Beyond Homework Help
Replies
18
Views
2K
Is There an Integration Factor for This Differential Equation?
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Finite Group G-set Stabiliser and Orbit: Orbits and Stabilisers Homework
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Showing that an element has order 2 if product of 2-cycles
    • Calculus and Beyond Homework Help
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top