To add polynomials {polynomial addition}, first put terms in simplest form. Then add coefficients of terms that have same variables with same exponents. Sums have same number of terms as total number of different terms in both polynomials.
polynomial division
To divide two polynomials, write polynomials with terms decreasing from highest exponent term. Divide smaller second-polynomial first term into larger first-polynomial first term. Multiply smaller polynomial by quotient. Subtract product from first polynomial. Divide difference by second-polynomial first term, to get new quotient. Then repeat steps. For example, (12*x^2 - x - 6) / (3*x + 2) = (4*x) * (3*x + 2) - 9*x - 6 = (4*x - 3) * (3*x + 2).
polynomial multiplication
To multiply polynomials, multiply each first-polynomial term by each second-polynomial term. Product-term number is number of first-polynomial terms times number of second-polynomial terms. Put terms in simplest form. Add coefficients of terms that have same variables with same exponents.
Mathematical Sciences>Algebra>Function>Kinds>Polynomial>Operations
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Date Modified: 2022.0224