Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem asks to find the value(s) of $x$ given that a rectangle $PQRS$ has two squares of side $...
Quadratic EquationsGeometryArea Calculation
2025/4/19
We are asked to factor the polynomial $4x^3 - 8x^2 - 36x - 72$.
Polynomial FactorizationCubic PolynomialsFactoring by GroupingDifference of Squares
2025/4/19
The problem asks to factorise the given expressions completely. We have two parts: (a) $8x^2(x-7) - ...
FactorizationPolynomialsQuadratic Equations
2025/4/19
We are asked to solve the equation $\frac{1}{x-3} + \frac{1}{x-4} = \frac{5}{x^2 - 7x + 12}$ for $x$...
Algebraic EquationsRational EquationsEquation SolvingFactorization
2025/4/19
Solve the equation $\frac{4}{x^2-8x} - \frac{3}{x^2+8x} = \frac{x}{x^2-64}$.
Rational EquationsQuadratic EquationsEquation SolvingFactorizationExtraneous Solutions
2025/4/19
The problem provides a universal set $U$, a set $A$, a function $f(x)$, and a function $P(y)$. The u...
Set TheoryPolynomialsIrrational NumbersFunctions
2025/4/19
The problem consists of two parts. (a) Solve the inequality $4 + \frac{3}{4}(x+2) \leq \frac{3}{8}x ...
InequalitiesQuadratic EquationsArea CalculationFactorization
2025/4/19
The problem consists of two parts. (a) Solve the inequality: $4 + \frac{3}{4}(x + 2) \le \frac{3}{8}...
InequalitiesArea CalculationQuadratic EquationsGeometry
2025/4/19
We are given a rectangle $PQRS$ with side lengths $PS = 20$ cm and $SR = 10 + x + 10 = 20 + x$ cm. A...
GeometryAreaQuadratic EquationsWord ProblemRectangleSquare
2025/4/19
The problem asks to simplify the expression $\frac{\sqrt{18}}{\sqrt{8}} \times \frac{\sqrt{20}}{\sqr...
RadicalsSimplificationExponents
2025/4/19