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In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [1] —hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: The general form is. Note that a is both a "first" term and an "outer" term; b is both a "last" and "inner" term, and so forth.
Finding the roots (zeros) of a given polynomial has been a prominent mathematical problem.. Solving linear, quadratic, cubic and quartic equations in terms of radicals and elementary arithmetic operations on the coefficients can always be done, no matter whether the roots are rational or irrational, real or complex; there are formulas that yield the required solutions.
Vieta's formulas relate the polynomial coefficients to signed sums of products of the roots r1, r2, ..., rn as follows: (*) Vieta's formulas can equivalently be written as for k = 1, 2, ..., n (the indices ik are sorted in increasing order to ensure each product of k roots is used exactly once). The left-hand sides of Vieta's formulas are the ...
All polynomials with coefficients in a unique factorization domain (for example, the integers or a field) also have a factored form in which the polynomial is written as a product of irreducible polynomials and a constant. This factored form is unique up to the order of the factors and their multiplication by an invertible constant.
Cubic equation. Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis at y = 0 ). The case shown has two critical points. Here the function is and therefore the three real roots are 2, -1 and -4. In algebra, a cubic equation in one variable is an equation of the form in which a is not zero.
Alternatively, Horner's method also refers to a method for approximating the roots of polynomials, described by Horner in 1819. It is a variant of the Newton–Raphson method made more efficient for hand calculation by the application of Horner's rule. It was widely used until computers came into general use around 1970.
Distributive property. In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality is always true in elementary algebra . For example, in elementary arithmetic, one has Therefore, one would say that multiplication distributes over addition .
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci ...