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For example, the number of times a given polynomial has a root at a given point is the multiplicity of that root. The notion of multiplicity is important to be able to count correctly without specifying exceptions (for example, double roots counted twice). Hence the expression, "counted with multiplicity".
This polynomial is further reduced to = + + which is shown in blue and yields a zero of −5. The final root of the original polynomial may be found by either using the final zero as an initial guess for Newton's method, or by reducing () and solving the linear equation. As can be seen, the expected roots of −8, −5, −3, 2, 3, and 7 were ...
In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...
The word polynomial joins two diverse roots: the Greek poly, meaning "many", and the Latin nomen, or "name". It was derived from the term binomial by replacing the Latin root bi-with the Greek poly-. That is, it means a sum of many terms (many monomials). The word polynomial was first used in the 17th century. [6]
For any polynomial q, the polynomial q + q ∗ is palindromic and the polynomial q − q ∗ is antipalindromic. It follows that any polynomial q can be written as the sum of a palindromic and an antipalindromic polynomial, since q = (q + q ∗)/2 + (q − q ∗)/2. [7] The product of two palindromic or antipalindromic polynomials is palindromic.
2. Words/expressions that can help ease tension and stress. 3. Related to a classic cocktail. 4. Elements of a famous brain teaser. Related: 300 Trivia Questions and Answers to Jumpstart Your Fun ...
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