Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem asks to find the slope of the line that passes through the points $(2, -4)$ and $(8, 0)$...
Linear EquationsSlopeCoordinate Geometry
2025/3/11
The problem presents a generating function $GF_n^{(s)}(x)$ and asks to find a closed-form expression...
Generating FunctionsSeriesClosed-form expressionComplex Numbers
2025/3/11
The problem asks us to factor the expression $(x^2-1)(x^3-1)(2x^2-x-1)$.
Polynomial FactorizationDifference of SquaresDifference of CubesFactoring by Grouping
2025/3/11
The problem is to solve the quadratic equation $2x^2 - 11x + 14 = 0$ for $x$.
Quadratic EquationsFactoringRoots of Equation
2025/3/11
We are given a sequence $a_n$ such that $a_1 = 2$ and $a_{n+1} = 3a_n + 4$. We need to find the gene...
Sequences and SeriesRecurrence RelationsGeometric SequencesAlgebraic Manipulation
2025/3/11
We are given two problems. The first problem asks us to find the inverse function $h^{-1}(y)$ of the...
Inverse FunctionsFunction TransformationsSquare Roots
2025/3/11
The first question asks us to find $g^{-1}(-8)$ given that $g(x) = x^3$ and $g(-2) = -8$. The second...
Inverse FunctionsFunction EvaluationApplied Functions
2025/3/11
We are given a sequence $\{a_n\}$ defined by the recurrence relation $a_{n+1} = 3a_n + 4$ with the i...
SequencesRecurrence RelationsGeometric SequencesAlgebraic Manipulation
2025/3/11
We are given a system of two linear equations: $4p + 2q = 62$ $8p - q = 59$ We need to determine if ...
System of Linear EquationsSolving EquationsLinear Algebra
2025/3/11
We are given a system of two linear equations in two variables, $x$ and $y$, and we need to find the...
System of Linear EquationsElimination MethodTwo Variables
2025/3/11