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  2. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial factorization of x 2 – 4. Factorization is not usually considered meaningful within number systems possessing division , such as the real or complex numbers , since any x {\displaystyle x} can be trivially written as ( x y ) × ( 1 / y ) {\displaystyle ...

  3. Factor theorem - Wikipedia

    en.wikipedia.org/wiki/Factor_theorem

    Out of these, the quadratic factor can be further factored using the quadratic formula, which gives as roots of the quadratic . Thus the three irreducible factors of the original polynomial are x + 1 , {\displaystyle x+1,} x − ( − 3 + 7 ) , {\displaystyle x-(-3+{\sqrt {7}}),} and x − ( − 3 − 7 ) . {\displaystyle x-(-3-{\sqrt {7}}).}

  4. Factorization of polynomials - Wikipedia

    en.wikipedia.org/wiki/Factorization_of_polynomials

    For univariate polynomials over the rationals (or more generally over a field of characteristic zero), Yun's algorithm exploits this to efficiently factorize the polynomial into square-free factors, that is, factors that are not a multiple of a square, performing a sequence of GCD computations starting with gcd(f(x), f '(x)). To factorize the ...

  5. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because it cannot be decomposed in this way. If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4).

  6. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    () = + is called the vertex form, where h and k are the x and y coordinates of the vertex, respectively. The coefficient a is the same value in all three forms. To convert the standard form to factored form, one needs only the quadratic formula to determine the two roots r 1 and r 2.

  7. Euler's factorization method - Wikipedia

    en.wikipedia.org/wiki/Euler's_factorization_method

    Even odd composite numbers of the form 4k + 1 are often the product of two primes of the form 4k + 3 (e.g. 3053 = 43 × 71) and again cannot be factored by Euler's method.

  8. What is a factor rate and how to calculate it - AOL

    www.aol.com/finance/factor-rate-calculate...

    A 1.35 factor rate is a mid-range rate lenders charge to borrow money. Factor rates typically fall between 1.1 and 1.5. With a 1.35 factor rate, it will cost $35,000 to borrow $100,000 ($100,000 x ...

  9. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    For example, let a denote a multiplicative generator of the group of units of F 4, the Galois field of order four (thus a and a + 1 are roots of x 2 + x + 1 over F 4. Because (a + 1) 2 = a, a + 1 is the unique solution of the quadratic equation x 2 + a = 0.