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  2. Rational root theorem - Wikipedia

    en.wikipedia.org/wiki/Rational_root_theorem

    q is an integer factor of the leading coefficient a n. The rational root theorem is a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials. The integral root theorem is the special case of the rational root theorem when the leading coefficient is a n = 1.

  3. Gaussian elimination - Wikipedia

    en.wikipedia.org/wiki/Gaussian_elimination

    So if two leading coefficients are in the same column, then a row operation of type 3 could be used to make one of those coefficients zero. Then by using the row swapping operation, one can always order the rows so that for every non-zero row, the leading coefficient is to the right of the leading coefficient of the row above.

  4. Coefficient - Wikipedia

    en.wikipedia.org/wiki/Coefficient

    Coefficient matrices are used in algorithms such as Gaussian elimination and Cramer's rule to find solutions to the system. The leading entry (sometimes leading coefficient [citation needed]) of a row in a matrix is the first nonzero entry in that row.

  5. Row echelon form - Wikipedia

    en.wikipedia.org/wiki/Row_echelon_form

    The leading entry (that is, the left-most nonzero entry) of every nonzero row, called the pivot, is on the right of the leading entry of every row above. [2] Some texts add the condition that the leading coefficient must be 1 [3] while others require this only in reduced row echelon form.

  6. Polynomial greatest common divisor - Wikipedia

    en.wikipedia.org/wiki/Polynomial_greatest_common...

    Note: "lc" stands for the leading coefficient, the coefficient of the highest degree of the variable. This algorithm computes not only the greatest common divisor (the last non zero r i), but also all the subresultant polynomials: The remainder r i is the (deg(r i−1) − 1)-th subresultant polynomial.

  7. Quartic equation - Wikipedia

    en.wikipedia.org/wiki/Quartic_equation

    There exists a general formula for finding the roots to quartic equations, provided the coefficient of the leading term is non-zero. However, since the general method is quite complex and susceptible to errors in execution, it is better to apply one of the special cases listed below if possible.

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  9. Limit of a function - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_function

    If the degree of p is greater than the degree of q, then the limit is positive or negative infinity depending on the signs of the leading coefficients; If the degree of p and q are equal, the limit is the leading coefficient of p divided by the leading coefficient of q; If the degree of p is less than the degree of q, the limit is 0.