Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

The problem asks to factor the quadratic expression $3x^2 + 2x - 1$.

Quadratic EquationsFactorizationAlgebraic Manipulation
2025/3/25

The problem asks to factor the trinomial $x^3 + x^2 - 72x$ completely. First, find the greatest comm...

Polynomial FactorizationGreatest Common FactorQuadratic Equations
2025/3/25

The problem asks to factor the polynomial $2x^2 + 20x + 18$. First, factor out the greatest common f...

Polynomial FactorizationQuadratic EquationsFactoringGreatest Common Factor
2025/3/25

The problem states that honey is distributed equally into jars. There are 16 jars with 24 kg of hone...

Linear EquationsWord ProblemProblem Solving
2025/3/25

We are given an expression involving the product of two fractions, each containing terms with $x$ an...

SimplificationExponentsFractionsVariables
2025/3/25

Simplify the expression $((-2xy^2)^2 (\frac{x^6}{(2x)^2})^3)$.

ExponentsSimplificationAlgebraic Expressions
2025/3/25

We are asked to simplify the expression $(-2x^2y^3z^4)(-4x^3yz^{-8})(5xy^2z^2)$.

PolynomialsExponentsSimplification
2025/3/25

The problem is to simplify the expression: $\frac{(10^2)^4 \times (5^3)^4}{(5^4)^2 \times (10^2)^5}$

ExponentsSimplificationFractional ExponentsOrder of Operations
2025/3/25

The problem defines a function $g(x) = \frac{1}{2} - \frac{3x}{1-x}$. We need to find: (i) $g(2)$ (i...

FunctionsInverse FunctionsFunction Evaluation
2025/3/25

The problem asks to find the inverse of the function $f$ which is defined as $f(x) = \frac{1}{3}(2x-...

FunctionsInverse FunctionsAlgebraic Manipulation
2025/3/25