A polynomial can be factored if it has a rational root.
If f(x) is a polynomial function of x and if there is a rational number p such that f(p) = 0 then
f(x) = (x-p)*g(x) where g(x) is a polynomial whose order is one less than the order of f(x).
If p = q/r where q and r are integers, then
(x - p) = (x - q/r) = (rx - q)/r which is a rational binomial factor. This does not work if p is irrational which is why p must be rational.
Not into rational factors.
A prime polynomial is a polynomial that cannot be factored into the product of two non-constant polynomials over its coefficient field. In other words, it has no divisors other than itself and the unit (constant) polynomials. For example, in the field of real numbers, (x^2 + 1) is a prime polynomial because it cannot be factored into real linear factors. Conversely, polynomials like (x^2 - 1) are not prime because they can be factored as ((x - 1)(x + 1)).
The laws of factoring polynomials include several key principles: First, identify common factors among terms to factor them out. Second, apply special factoring techniques, such as the difference of squares, perfect square trinomials, and the sum or difference of cubes. Third, use the quadratic formula or factoring by grouping for polynomials of higher degrees. Lastly, always check for irreducibility, ensuring the polynomial is factored completely.
Descartes did not invent polynomials.
That would be (x - 2) ( x - 5) ( x - 5). If you like, you can multiply these polynomials to get a single polynomial in standard form (i.e., not factored).
Not into rational factors.
A strategy that would be appropriate in factoring polynomials with 4 terms would be by grouping where you first determine if the polynomial can be factored by a group.
Other polynomials of the same, or lower, order.
Reducible polynomials.
they have variable
P. K. Suetin has written: 'Polynomials orthogonal over a region and Bieberbach polynomials' -- subject(s): Orthogonal polynomials 'Series of Faber polynomials' -- subject(s): Polynomials, Series
In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) are a class of classical orthogonal polynomials.
Descartes did not invent polynomials.
what is the prosses to multiply polynomials
That would be (x - 2) ( x - 5) ( x - 5). If you like, you can multiply these polynomials to get a single polynomial in standard form (i.e., not factored).
how alike the polynomial and non polynomial
Multiply the first and last coefficients.2*3=6What two factors give you six but when combined give you -5-2 and -3Therefore2x-3)(x-1) will be the factored model.