f(x)=x^3+px^2+qx+6
this formula can also be written in "factorised form" that is,
f(x)=a(x+b)(x+c)(x+d)
can someone please teach me how to change a funtion into it's factorised form?
thanks
the following link has some nice step-by-steps illustrations and examples
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut7_factor.htm
thanks!
To change a function into its factorized form, you need to follow these steps:
1. Start by finding the factors of the constant term (in this case, 6).
- In this example, the constant term is 6, so you need to find all the pairs of numbers that multiply to give 6. For example, pairs like (1, 6), (-1, -6), (2, 3), (-2, -3).
2. Next, find the factors of the leading coefficient (in this case, 1).
- In this example, the leading coefficient is 1, which means that you don't need to consider the factors of it.
3. Use the factors you found to create possible combinations for the polynomial.
- For example, if you found the pairs (1, 6), (-1, -6), (2, 3), (-2, -3), you can try different combinations like (x + 1)(x + 6)(x + 1), (x - 2)(x + 3)(x - 1), etc.
4. Simplify and expand the polynomial expression you obtained from step 3. You can use FOIL or distributive property to do this.
- For example, if you have (x + 1)(x + 6)(x + 1), expand it using FOIL to get (x^2 + 7x + 6)(x + 1). Then, multiply it again using FOIL to get x^3 + 8x^2 + 13x + 6.
5. Compare the expanded polynomial you obtained from step 4 with the original function.
- In this example, compare the expanded polynomial, x^3 + 8x^2 + 13x + 6, with the original function, x^3 + px^2 + qx + 6. You can equate the coefficients of the corresponding terms to find the values of p, q, and the constants in the factorized form.
By following these steps, you can convert a function into its factorized form. The link you provided, http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut7_factor.htm, contains detailed illustrations and examples that can further help you understand the process.