| 48 | Roots without solving | Medium | Lemma | Vieta's formulasSymmetric functions | |
| 106 | A remainder without dividing | Medium | Lemma | Remainder theorem | |
| 1172 | Division of Polynomial with Cube Root Coefficients | Medium | Hall & Knight | Polynomial divisionCube roots+1 | |
| 1214 | Cubic Equation with Parameter | Medium | Hall & Knight | Polynomial equationsRoots of polynomials+1 | |
| 1215 | Cubic Equation with Surd Roots | Medium | Hall & Knight | Polynomial equationsSurds+1 | |
| 1285 | Reciprocal Quartic Equation | Medium | Hall & Knight | palindromic polynomialsubstitution+1 | |
| 1377 | Divisibility of difference of powers | Medium | Hall & Knight | mathematical inductiondivisibility | |
| 1393 | Twenty-eighth term of binomial power | Medium | Hall & Knight | Binomial TheoremCombinations | |
| 1395 | Fifth term with fractional binomial | Medium | Hall & Knight | Binomial TheoremFractions | |
| 1404 | Coefficient of a power in expansion | Medium | Hall & Knight | Binomial TheoremGeneral Term | |
| 1405 | Coefficient of power with two variables | Medium | Hall & Knight | Binomial TheoremGeneral Term | |
| 1411 | Greatest term of binomial expansion | Medium | Hall & Knight | binomial theoremgreatest term | |
| 1412 | Greatest term with coefficients | Medium | Hall & Knight | binomial theoremgreatest term | |
| 1413 | Greatest term of binomial | Medium | Hall & Knight | binomial theoremgreatest term | |
| 1414 | Twin greatest terms | Medium | Hall & Knight | binomial theoremgreatest term | |
| 1415 | Value of greatest term | Medium | Hall & Knight | binomial theoremgreatest term | |
| 1416 | Value of twin greatest terms | Medium | Hall & Knight | binomial theoremgreatest term | |
| 1417 | Middle terms of binomial expansions | Medium | Hall & Knight | Binomial TheoremBinomial coefficients | |
| 1418 | Sum of odd and even terms | Medium | Hall & Knight | Binomial TheoremAlgebraic identities | |
| 1419 | Finding parameters from binomial terms | Medium | Hall & Knight | Binomial TheoremSystems of equations | |
| 1420 | Expansion of a trinomial | Medium | Hall & Knight | Binomial TheoremMultinomial expansion | |
| 1421 | Cubic expansion of a quadratic trinomial | Medium | Hall & Knight | Binomial TheoremPolynomials | |
| 1422 | Term from the end of a binomial expansion | Medium | Hall & Knight | Binomial TheoremGeneral term | |
| 1525 | Coefficient of x^32 in reciprocal binomial | Medium | Hall & Knight | Binomial TheoremGeneral Term | |
| 1526 | Coefficient of x^-17 in reciprocal binomial | Medium | Hall & Knight | Binomial TheoremGeneral Term | |
| 1527 | First middle term of binomial expansion | Medium | Hall & Knight | Binomial TheoremMiddle Terms | |
| 1528 | Second middle term of binomial expansion | Medium | Hall & Knight | Binomial TheoremMiddle Terms | |
| 1722 | Divisibility condition by undetermined coefficients | Medium | Hall & Knight | polynomial divisibilityundetermined coefficients+1 | |
| 1723 | Conditions for a Bivariate Quadratic Square | Medium | Hall & Knight | undetermined coefficientspolynomials+1 | |
| 1724 | Cubic Divisible by Quadratic Sum of Squares | Medium | Hall & Knight | undetermined coefficientspolynomial division+1 | |
| 1725 | Quintic Divisible by a Squared Linear Factor | Medium | Hall & Knight | undetermined coefficientsdivisibility+1 | |
| 1731 | Cubic Denominator Series Expansion | Medium | Hall & Knight | undetermined coefficientspower series expansion | |
| 1739 | Partial Fraction Decomposition with Difference of Squares | Medium | Hall & Knight | partial fractionsrational functions | |
| 1741 | Partial Fractions with Improper Rational Function | Medium | Hall & Knight | partial fractionspolynomial division | |
| 1742 | Partial Fractions with Repeated Linear Factor | Medium | Hall & Knight | partial fractionsrepeated roots | |
| 1743 | Partial Fraction Decomposition of Quartic | Medium | Hall & Knight | partial fractionspolynomial division | |
| 1746 | Repeated Linear Factor Decomposition | Medium | Hall & Knight | partial fractionsrepeated roots | |
| 1747 | Complex Repeated Factors | Medium | Hall & Knight | partial fractionssimplification | |
| 1824 | Sum of Multinomial Coefficients | Medium | Hall & Knight | binomial theorempolynomial coefficients+1 | |
| 1885 | Lagrange Interpolation Identity Quadratic | Medium | Hall & Knight | undetermined coefficientsidentities+1 | |
| 1886 | Lagrange Interpolation Identity Cubic | Medium | Hall & Knight | undetermined coefficientsidentities+1 | |
| 1906 | Factorization of a symmetric product | Medium | Hall & Knight | FactorisationSymmetric polynomials | |