Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
We are given the equation $x^2 + xy + y^2 = 6$. We are asked to solve this equation, but it is not s...
Quadratic EquationsReal SolutionsInequalitiesSolution Sets
2025/3/21
Solve the equation $4x^2 - 4y^2 - 2x + 2y + 1 = 0$.
Quadratic EquationsConic SectionsHyperbolaCompleting the Square
2025/3/21
The problem asks to find one root of the equation $x^3 + 2x - 3x^2 - 6 = 0$. The possible roots are ...
Polynomial EquationsRootsCubic EquationsTesting Roots
2025/3/20
The problem asks which of the following binomials is a factor of the polynomial $x^3 - 6x^2 + 11x - ...
PolynomialsFactor TheoremPolynomial FactorizationRoots of Polynomials
2025/3/20
The problem asks to find one root of the cubic equation $x^3 + 2x - 3x^2 - 6 = 0$ from the given opt...
Polynomial EquationsCubic EquationsRoot FindingFactorization
2025/3/20
We are asked to find the remainder when the polynomial $x^2 + 3x$ is divided by $x$.
Polynomial DivisionRemainder TheoremPolynomial Factorization
2025/3/20
The problem asks us to find the remainder when the polynomial $x^4 + 2x^2 - 3x + 7$ is divided by $x...
PolynomialsRemainder TheoremPolynomial Division
2025/3/20
The problem asks us to find which of the given binomials is a factor of the polynomial $x^3 - 6x^2 +...
PolynomialsFactor TheoremPolynomial Factorization
2025/3/20
The problem asks to determine the completely factored form of the polynomial $f(x) = x^3 + 5x^2 - x ...
Polynomial FactorizationFactoring by GroupingDifference of SquaresCubic Polynomials
2025/3/20
We are given that $x=2$ is a root of the equation $4x^3 + kx - 24 = 0$. We need to find the value of...
Polynomial EquationsRoot of an EquationSubstitutionSolving for a Variable
2025/3/20