Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem asks to find the remainder when the polynomial $f(x) = x^4 + 3x^3 - 4x^2 + 3x + 6$ is di...
PolynomialsRemainder TheoremPolynomial Division
2025/4/19
Given that $\alpha$ and $\beta$ are the roots of the quadratic equation $3x^2 - 5x + 1 = 0$, we need...
Quadratic EquationsRoots of EquationsVieta's Formulas
2025/4/19
We are given the equation $\log_y(2x+3) + \log_y(2x-3) = 1$, and we are asked to find an expression ...
LogarithmsEquationsAlgebraic Manipulation
2025/4/19
The problem asks us to find the quadratic equation given the sum and product of its roots. The sum o...
Quadratic EquationsRoots of EquationsSum and Product of Roots
2025/4/19
We need to simplify the expression $(216)^{\frac{2}{3}} \times (0.16)^{-\frac{3}{2}}$.
ExponentsSimplificationFractional ExponentsOrder of Operations
2025/4/19
The problem asks us to find the coefficient of $x^4$ in the expansion of $(1-2x)^6$.
Binomial TheoremPolynomial ExpansionCombinatoricsCoefficients
2025/4/19
Find the minimum value of the quadratic function $2x^2 - 8x + 3$.
Quadratic FunctionsCompleting the SquareVertex of a ParabolaOptimization
2025/4/19
We are given a system of two linear equations with two variables, $x$ and $y$. We need to find the v...
Linear EquationsSystems of EquationsElimination MethodVariables
2025/4/19
Solve the following system of linear equations: $6x - 3y = 39$ $-3x - 8y = 39$
Linear EquationsSystems of EquationsElimination Method
2025/4/19
We need to solve the quadratic equation $7x^2 - 6x - 3 = 0$ for $x$.
Quadratic EquationsQuadratic FormulaRoots of EquationsAlgebra
2025/4/19