Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
Simplify the expressions by removing the brackets. The given expressions are: (a) $(a4^3)^2$ (b) $(x...
ExponentsSimplificationPolynomials
2025/4/16
The problem asks us to simplify the given expressions by removing the brackets. The expressions are:...
ExponentsPolynomialsSimplificationAlgebraic Expressions
2025/4/16
The problem is to simplify algebraic expressions by removing the brackets. The expressions are: (a) ...
Algebraic ExpressionsSimplificationExponentsPolynomialsPower of a PowerProduct of PowersDistributive Property
2025/4/16
We are given the polynomial $P(x) = x^3 - px + q$. When $P(x)$ is divided by $x^2 - 3x + 2$, the rem...
Polynomial DivisionRemainder TheoremSystem of Equations
2025/4/16
We are given the quadratic equation $x^2 + (k-2)x + 10 - k = 0$. We need to find the range of values...
Quadratic EquationsDiscriminantInequalitiesReal RootsInterval Notation
2025/4/16
We are given that the second term of a geometric sequence is 4 and the fourth term is 8. We are aske...
Sequences and SeriesGeometric SequenceCommon RatioFinding the nth term
2025/4/16
We are asked to find the minimum value of the quadratic function $2x^2 - 8x + 3$.
Quadratic FunctionsOptimizationCompleting the SquareVertex Formula
2025/4/16
We are given the function $f(x) = 6x^3 + px^2 + 2x - 5$, where $p$ is a constant. We also know that ...
PolynomialsFunction EvaluationSolving Equations
2025/4/16
We are asked to simplify the expression $\frac{\log 9 - \log 8}{\log 81 - \log 64}$.
LogarithmsSimplificationLogarithm Properties
2025/4/16
We are asked to evaluate the expression: $log\ 9 - log\ 8$ $log\ 81 - log\ 64$
LogarithmsLogarithmic PropertiesSimplification
2025/4/16