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