Algebra · Chapter 7 of 20

Polynomials

79 curated · 2,980 from open sources · 6.5 million generated

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Expand a product of binomialsEasy · 6.5 million variations

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#	Title	Difficulty	Source	Tags
751	The remainder theorem	Easy	Lemma	Polynomials
752	Multiply it out	Easy	Lemma	Polynomials
753	Make it a factor	Easy	Lemma	Polynomials
754	Sum of coefficients	Easy	Lemma	Polynomials
1213	Cubic Equation from Three Roots	Easy	Hall & Knight	Polynomial equationsRoots of polynomials+1
1378	Binomial Expansion of (x-3)^5	Easy	Hall & Knight	Binomial Theorem
1379	Binomial Expansion of (3x+2y)^4	Easy	Hall & Knight	Binomial Theorem
1380	Binomial Expansion of (2x-y)^5	Easy	Hall & Knight	Binomial Theorem
1381	Binomial Expansion of (1-3a^2)^6	Easy	Hall & Knight	Binomial Theorem
1382	Binomial Expansion of (x^2+x)^5	Easy	Hall & Knight	Binomial Theorem
1383	Binomial Expansion of (1-xy)^7	Easy	Hall & Knight	Binomial Theorem
1390	Fourth term of binomial power	Easy	Hall & Knight	Binomial TheoremExpansion
1391	Tenth term of binomial power	Easy	Hall & Knight	Binomial TheoremExpansion
1392	Twelfth term of binomial power	Easy	Hall & Knight	Binomial TheoremExpansion
1394	Fourth term with fractions	Easy	Hall & Knight	Binomial TheoremFractions
1402	Middle term of a binomial	Easy	Hall & Knight	Binomial TheoremMiddle Term
1403	Middle term of negative power binomial	Easy	Hall & Knight	Binomial TheoremMiddle Term
1728	Series Expansion via Undetermined Coefficients	Easy	Hall & Knight	undetermined coefficientspower series expansion
1729	Rational Function Expansion to Cubic Term	Easy	Hall & Knight	undetermined coefficientspower series expansion
1730	Ascending Power Series Expansion	Easy	Hall & Knight	undetermined coefficientspower series expansion
1737	Partial Fraction Decomposition Quadratic Denominator	Easy	Hall & Knight	partial fractionsrational functions
1738	Partial Fraction Decomposition with Linear Factors	Easy	Hall & Knight	partial fractionsrational functions
1740	Partial Fractions with Three Linear Factors	Easy	Hall & Knight	partial fractionsrational functions
1744	Partial Fractions with Quadratic Factor	Easy	Hall & Knight	partial fractionsquadratic denominator
1745	Partial Fractions with Irreducible Quadratic	Easy	Hall & Knight	partial fractionsirreducible quadratic
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
1203	Symmetric Product of Linear Forms	Deep	Hall & Knight	algebraic identitycube roots of unity+1
1286	Symmetric Quartic Equation	Deep	Hall & Knight	symmetric equationssubstitution+1
1301	Fourth Degree Polynomial Equation	Deep	Hall & Knight	Polynomial factorizationCompleting the square
1302	Cubic Equation	Deep	Hall & Knight	Cubic equationsFactorization
1556	Thirds of Trinomial Expansion Coefficients	Deep	Hall & Knight	cube roots of unitypolynomial expansion+1
1726	Condition for Quadratic Factorability	Deep	Hall & Knight	undetermined coefficientsfactorization+1
1727	Sum of Products of Powers	Deep	Hall & Knight	symmetric functionsseries of powers
1757	Homogeneous products of three variables	Deep	Hall & Knight	generating functionspartial fractions+1
1825	Weighted Sum of Coefficients	Deep	Hall & Knight	polynomial differentiationidentities
1898	Symmetric functions of powers	Deep	Hall & Knight	Symmetric functionsGeometric series
1904	Algebraic Identity Verification	Deep	Hall & Knight	algebraic identitiespolynomial manipulation
1907	Identity with fourth powers	Deep	Hall & Knight	Algebraic identitiesSymmetric functions

From open sources

2,980

Showing everything, including problems with no answer to check, a missing figure, or a near-copy elsewhere. Show only complete problems

#	Title	Difficulty
99601	Identifying the Degree and Leading Coefficient of a Polynomial	Easy
99602	Polynomials · Try It 1	Easy
99603	Adding Polynomials	Easy
99605	Subtracting Polynomials	Easy
99607	Multiplying Polynomials Using the Distributive Property	Easy
99611	Expanding Perfect Squares	Easy
99613	Multiplying Binomials Resulting in a Difference of Squares	Easy
99615	Multiplying Polynomials Containing Several Variables	Easy
99617	Polynomials · Exercise 1	Easy
99619	Polynomials · Exercise 3	Easy
101658	Power Functions and Polynomial Functions · Example 1	Easy
101660	Power Functions and Polynomial Functions · Example 2	Easy
101661	Power Functions and Polynomial Functions · Example 3	Easy
101668	Identifying Power Functions	Easy
101669	Power Functions and Polynomial Functions · Try It 1	Easy
101672	Power Functions and Polynomial Functions · Try It 2	Easy
101673	Identifying Polynomial Functions	Easy
101674	Identifying the Degree and Leading Coefficient of a Polynomial Function	Easy
101675	Power Functions and Polynomial Functions · Try It 3	Easy
101676	Identifying End Behavior and Degree of a Polynomial Function	Easy
101677	Power Functions and Polynomial Functions · Try It 4	Easy
101680	Power Functions and Polynomial Functions · Try It 5	Easy
101681	Determining the Number of Intercepts and Turning Points of a Polynomial	Easy
101682	Power Functions and Polynomial Functions · Try It 6	Easy
101683	Drawing Conclusions about a Polynomial Function from the Factors	Easy
101684	Power Functions and Polynomial Functions · Try It 7	Easy
101685	Power Functions and Polynomial Functions · Exercise 8	Easy
101687	Power Functions and Polynomial Functions · Exercise 10	Easy
101689	Power Functions and Polynomial Functions · Exercise 12	Easy
101701	Power Functions and Polynomial Functions · Exercise 24	Medium
101704	Power Functions and Polynomial Functions · Exercise 28	Medium
101706	Power Functions and Polynomial Functions · Exercise 30	Medium
101708	Power Functions and Polynomial Functions · Exercise 32	Medium
101710	Power Functions and Polynomial Functions · Exercise 34	Medium
101712	Power Functions and Polynomial Functions · Exercise 36	Medium
101715	Power Functions and Polynomial Functions · Exercise 54	Medium
101717	Power Functions and Polynomial Functions · Exercise 56	Medium
101746	Solve a quadratic equation by factoring	Easy
101749	Solve a quadratic equation by factoring	Easy
101757	Finding the y- and x-Intercepts of a Polynomial in Factored Form	Easy
101759	Graphs of Polynomial Functions · Try It 1	Easy
101763	Using the Intermediate Value Theorem	Easy
101764	Graphs of Polynomial Functions · Try It 3	Easy
101766	Graphs of Polynomial Functions · Try It 4	Easy
101767	Graphs of Polynomial Functions · Exercise 15	Easy
101769	Graphs of Polynomial Functions · Exercise 17	Easy
101773	Graphs of Polynomial Functions · Exercise 21	Medium
101781	Graphs of Polynomial Functions · Exercise 29	Medium
101783	Graphs of Polynomial Functions · Exercise 31	Medium
101787	Graphs of Polynomial Functions · Exercise 35	Medium