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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.
What else can I help you with?
Can all cubic polynomials be factored into polynomials of degree 1 or 2?
Not into rational factors.
What is a prime polynomial?
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)).
What are the laws of factoring polynomials?
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.
What is a polynomial with a single root at x equals 2 and a double root at x equals 5?
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).
Where did René Descartes invent polynomials?
Descartes did not invent polynomials.
Can all cubic polynomials be factored into polynomials of degree 1 or 2?
Not into rational factors.
What strategies is appropriate for factoring polynomials with 4 terms?
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.
What is a prime polynomial?
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)).
What are the laws of factoring polynomials?
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.
Polynomials have factors that are?
Other polynomials of the same, or lower, order.
What are polynomials that have factors called?
Reducible polynomials.
How polynomials and non polynomials are alike?
they have variable
What has the author P K Suetin written?
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
What is a jocobi polynomial?
In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) are a class of classical orthogonal polynomials.
Why do we need to factor polynomials?
Factoring polynomials is essential because it simplifies complex expressions, making them easier to solve or analyze. Factored forms can reveal the roots or zeros of the polynomial, which are crucial for graphing and understanding its behavior. Additionally, factoring is a fundamental skill in algebra that facilitates more advanced topics, such as calculus and differential equations. Overall, it enhances mathematical problem-solving efficiency and clarity.
What is a polynomial with a single root at x equals 2 and a double root at x equals 5?
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).
Where did René Descartes invent polynomials?
Descartes did not invent polynomials.
