Factorising x^3 + 216 to Include (x + 6)

  • Thread starter Alkatran
  • Start date
  • Tags
    Roots
In summary, factorising an equation means expressing it as a product of its factors to simplify it for solving. This is done by identifying common factors and using algebraic techniques such as the distributive property or grouping. The inclusion of (x + 6) in the factorisation of x^3 + 216 allows for easier simplification and finding of roots. The purpose of factorising an equation is to solve it, simplify expressions, and understand the structure better. While not all equations can be factorised, most polynomial equations can be using algebraic techniques.
  • #1
Alkatran
Science Advisor
Homework Helper
959
0
I need to factorise x^3 + 216 to include (x+6):

(x + 6) \ (x^3 + 216) (lim where x approaches -6)

I broke it down to (x + 6i)(x^2 - 36i) ... but that's no good.
 
Physics news on Phys.org
  • #2
Well, shouldn't polynomial division work fine?
 
  • #3
Remember

[tex] X^3 + Y^3 = (X+Y)(X^2-XY+Y^2) [/tex]
 
  • #4
He has

[tex] \frac{x+6}{x^3 + 216} [/tex]

[tex] \frac{x+6}{x^3 + 6^3} [/tex]
 
  • #5
I got it fine before I even came back. I was trying to remember how to do long division and the cube rule that you guys posted. The start of the year, still getting restarted...
 

1. What does it mean to "factorise" an equation?

Factorising an equation means to express it as a product of its factors. It is a way of simplifying an equation and making it easier to solve.

2. How do you factorise an equation?

To factorise an equation, you need to look for common factors and use algebraic techniques such as the distributive property or grouping to express the equation as a product of its factors. In the case of x^3 + 216, we can factor out a common factor of (x + 6) to simplify the equation.

3. What is the significance of including (x + 6) in the factorisation of x^3 + 216?

By including (x + 6) in the factorisation, we are expressing the equation as a product of (x + 6) and another factor, which in this case is x^2 - 6x + 36. This allows us to simplify the equation and find the roots (values of x that make the equation equal to 0) more easily.

4. What is the purpose of factorising an equation?

Factorising an equation is useful for solving equations, simplifying expressions, and finding the roots of an equation. It also allows us to see the relationship between different terms in an equation and understand the structure of the equation better.

5. Can you factorise any equation?

Not all equations can be factorised, but most polynomial equations (equations with multiple terms including variables raised to different powers) can be factorised using algebraic techniques. However, some equations may require more advanced mathematical methods to be solved.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
Replies
2
Views
697
  • Precalculus Mathematics Homework Help
Replies
6
Views
545
  • Introductory Physics Homework Help
Replies
11
Views
998
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
758
  • Precalculus Mathematics Homework Help
Replies
2
Views
465
  • Introductory Physics Homework Help
Replies
4
Views
209
  • Precalculus Mathematics Homework Help
Replies
13
Views
758
  • Introductory Physics Homework Help
Replies
18
Views
2K
Back
Top