In today's math for all chapter we teach you how to factorize third-degree or higher polynomials using the Ruffini method. The idea of this method is to look for the roots of the polynomial and we will proceed to test with different x's until Ruffini gives us 0. A trick is to use only the divisors of the independent term.
Once we have a root we have to express the factorization in this way:
(x-root1)*(quotient of the polynomial divided by (x-root1) calculated by Ruffini)
If the polynomial quotient has a degree greater than 2 we will reapply Ruffini to get a new root, factoring in the same way and adding the new root to the previous factorization along with the new calculated quotient.
(x-root1)*(x-root2)*(quotient of the polynomial divided by (x-root) calculated by Ruffini)
This process will be repeated until the polynomial quotient is irreducible. If the polynomial is second degree I recommend solving it by the traditional second degree equation method as it is more effective.
IMPORTANT: Don't forget that if the polynomial quotient we factored in the last step by calculating its roots has a coefficient (in the x of highest degree) different to 1, it should be included as a product in the factorization.
Негізгі бет Factorization of polynomials of grade 2,3,4...(Ruffini method)
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