What is the definition of a polynomial?
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That is a lady named Polly who doesn't have any meal.  This true fact is unknown to many mathematicians.
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Let r be an element if R, and hence in L.  Since L is an algebraic extension of K, all elements of L, there is an irreducible polynomial:\n\n    P(x) = a0 + a1x + a2x^2 + ... anx^n\n\nwith the ai's in K such P(r) = 0.\n\nSubtracting a0 from both sides, we see:\n\n    -a0 = r ( a1 + a2r + a3r^2 .. + anr^(n-1))\n\nDividing both sides by -a0 we get (a0 is not zero because P is irreducible):\n\n      1 = r (-a1/a0 - a2/a0 r - a3/a0 r^2 ...)\n\nThe right side is in R since the the coefficients -ai/a0 are in K and r is in r.  So we have an inverse of r in R.
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D ( 2 or 0)\n\nThis is because the coefficients of the given cubic polynomial are real numbers and so any real zero needs be accompanied by its complex conjugate and so as stated  earlier MUST come in pairs so either there are 2 or there cannot be any.
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Factoring, I guess, but it really depends on the type of polynomial question. Can you give a sample?
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In this polynomial: a=6, b=-2, c=-20.\nSub a, b, and c into this equation: \nx= [-b+ square root the whole thing that inside this bracket(b*b -4ac)]/2a\n\nx'= [-b - square root the whole thing that inside this bracket(b*b -4ac)]/2a
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Polynomials are expressions involving x raised to a whole number power (exponent). Some examples are: \n\n\n\nIn this lesson we consider division of polynomials such as: \n and . \nThere are two ways to calculate a division of polynomials. One is long division and a second method is called synthetic division. Synthetic division can be used when the polynomial divisor such as x-2 has the highest power of x as 1 and the coefficient of x is also 1. Otherwise, such as , a long division process must be used. Both methods will be demonstrated. \n\nWe will now look at some examples showing how these two procedures are done
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Neville's algorithm is an algorithm used to construct unique, interpolating polynomials. It uses n + 1 points to construct polynomials of degree n.\n\nIt is similar to Aitken's algorithm, which is nowadays not used.
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This would most definitely be a polynomial function, since it starts with x cubed. Anything that has x cubed or higher in it, like x to the fifth power, would be a polynomial function. An equation with x squared would be a quadratic function. An equation with just x would be a linear equation.
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Domain lists all possible x values. A normal polynomial function has a domain of all real numbers, because EVERY x value works.\n\nYour task is to find x values that DON'T work...and since you cannot divide by zero, then any x in the denominator that makes x^4+1 equal to zero will not be part of the domain.\n\nSo, what do you know about x^4+1?\n\nIt is an even power, so even if you put a negative number in for x, x^4+1 will be positive (since adding one will only make it more positive). If x=0, that is still positive, because of the plus one.\n\nx^4+1 is ALWAYS positive for any x...therefore it is NEVER equal to zero. Therefore any x value works, and your answer is all real numbers!!
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Nope.  Example: "1" is a polynomial "x" is also a polynomial (these are simple polynomials).  But "1/x" is not a polynomial.\n\nPolynomials divided by polynomials are always rational functions.
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There is a theorem related to polynomial divisions called the remainder theorem. Let p(x) be a polynomial of any degree. When it is divided by a linear polynomial of the form x - a, the remainder is p(a).\nAnswer 1:\nLet p(x) = x^5 - 3x^3 + x^2 - 3\nDivisor = x - 2\nHere, a = 2\np(2) = 2^5 - 3(2)^3 + 2^2 - 3\n= 32 - 24 + 4 - 3\n= 32 - 24 + 1\n= 8 + 1   \n= 9\n\nAnswer 2:\np(x) = x^5 - 3x^3 + x^2 - 3\nDivisor = x + 1\na = -1\np(-1) = (-1)^5 -3(-1)^3 + (-1)^2 - 3\n= -1 + 3 + 1 - 3\n= 0\n\nYou can check with actual division if you like. Looks like some of us have it wrong.
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depends what your trying to sum from the polynomial... what are you trying to get, theres to many thing just to say sum of given polynomials
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Factoring Polynomials \nFactoring Polynomials. Factoring a polynomial is the opposite process of multiplying polynomials. ... looking for simpler polynomials that can be ...www.jamesbrennan.org/algebra/polynomials/factoring_polynomials.htm - 16k - Cached - More from this site \nFactoring Polynomials \nFactoring Polynomials. by Shelley Walsh ©2000. Common Factors ... How to Add, Subtract, Multiply, and Divide Polynomials. Synthetic Division ...faculty.ed.umuc.edu/~swalsh/Math Articles/Factoring.html
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its a polynomial, constant or something like that. or a cow
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The easiest function of x are:\n\nf(x) = constant\nf(x) = a*x, where a is a constant : 1st order poly\nf(x) = b*x^2 where b is a constant 2nd order\nf(x) = c*x^3 where c is a constant: 3rd order\n...\nf(x) = z*x^n, where z is a constant, n is a positive integer, nth order polynomial\n\na general polynomial is a sum of these.  They are convenient to work with for lots of reasons.  That's why they are so important.
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Look in your text book under "factoring polynomials"... or you could try this web site that explains this fairly thoroughly...\n\nhttp://faculty.ed.umuc.edu/~swalsh/Math%20Articles/Factoring.html
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Do you mean "zero of a polynomial?" If so, then read on...\n\nA zero of a polynomial is the value or values of the variable (usually x) that cause the polynomial to equal zero.\n\nExample 1: The zero of the monomial 3*x is 0 because 3*0 is zero.\n\nExample 2: The binomial x + 2 has it's zero at x = -2 because if you substitute -2 in place of x, then you get \n---> -2 + 2 = 0.\nTherefore, -2 is the zero of the given binomial.\n\nExample 3: Find the zeros of the trinomial x^2 - x - 6. That is, solve x^2 - x - 6 = 0. If you factor the trinomial, then you get \n---> (x + 2)(x - 3) = 0. \nIn this problem there are two possibilities. Either \n---> x + 2 = 0  or  x - 3 = 0. \nSolving each gives x = -2 or x = 3. Therefore, the zeros of the given trinomial are -2 and 3. \n\nIf you substitute -2 into the given trinomial, then you have the following:\nx^2 - x - 6 \n= (-2)^2 - (-2) - 6 \n= 4 + 2 - 6\n= 6 - 6\n= 0 \n\nIf you substitute 3 into the given trinomial, then you have the following:\nx^2 - x - 6 \n= (3)^2 - (3) - 6 \n= 9 - 3 - 6\n= 6 - 6\n= 0 \n\nThere are no other values of x that will cause our given trinomial to equal zero.\n\nDefinitions\nA monomial is a polynomial with one term.\nA binomial is a polynomial with two terms.\nA trinomial is a polynomial with three terms.\nA polynomial with more than three terms is just called a polynomial.\n\nNote: If you graph a polynomial, then the graph will touch or cross the x-axis at the zeros of the polynomial. Zeros of a polynomial are also called solutions, roots, and, in some cases, x-intercepts.