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  2. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). All of the roots of the cubic equation can be found by ...

  3. Factorization of polynomials - Wikipedia

    en.wikipedia.org/wiki/Factorization_of_polynomials

    In particular, if there is exactly one non-linear factor, it will be the polynomial left after all linear factors have been factorized out. In the case of a cubic polynomial, if the cubic is factorizable at all, the rational root test gives a complete factorization, either into a linear factor and an irreducible quadratic factor, or into three ...

  4. Cubic function - Wikipedia

    en.wikipedia.org/wiki/Cubic_function

    In mathematics, a cubic function is a function of the form () = + + +, that is, a polynomial function of degree three. In many texts, the coefficients a , b , c , and d are supposed to be real numbers , and the function is considered as a real function that maps real numbers to real numbers or as a complex function that maps complex numbers to ...

  5. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    In elementary algebra, factoring a polynomial reduces the problem of finding its roots to finding the roots of the factors. Polynomials with coefficients in the integers or in a field possess the unique factorization property, a version of the fundamental theorem of arithmetic with prime numbers replaced by irreducible polynomials.

  6. Solution in radicals - Wikipedia

    en.wikipedia.org/wiki/Solution_in_radicals

    A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition, subtraction, multiplication, division, raising to integer powers, and extraction of n th roots (square roots, cube roots, etc.). A well-known example is the quadratic formula

  7. Factorization of polynomials over finite fields - Wikipedia

    en.wikipedia.org/wiki/Factorization_of...

    Polynomial factoring algorithms use basic polynomial operations such as products, divisions, gcd, powers of one polynomial modulo another, etc. A multiplication of two polynomials of degree at most n can be done in O(n 2) operations in F q using "classical" arithmetic, or in O(nlog(n) log(log(n)) ) operations in F q using "fast" arithmetic.

  8. 10 Hard Math Problems That Even the Smartest People in the ...

    www.aol.com/10-hard-math-problems-even-150000090...

    Having a factor of 3 means a number isn’t prime (with the sole exception of 3 itself). ... It turns out functions like this have certain properties that cast insight into math topics like ...

  9. Polynomial long division - Wikipedia

    en.wikipedia.org/wiki/Polynomial_long_division

    The result R = 0 occurs if and only if the polynomial A has B as a factor. Thus long division is a means for testing whether one polynomial has another as a factor, and, if it does, for factoring it out. For example, if a root r of A is known, it can be factored out by dividing A by (x – r).

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