Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem asks us to rewrite the quadratic expression $x^2 - 2x - 4$ in the form $(x + c)^2 + d$ a...
Quadratic EquationsCompleting the SquareEquation Solving
2025/5/12
We need to solve two inequalities involving square roots. (g) $\sqrt{2x+5} < \sqrt{9+x}$ (h) $\sqrt{...
InequalitiesSquare RootsAlgebraic Manipulation
2025/5/11
We need to solve the following inequalities: (a) $10 - \sqrt{2x+7} \le 3$ (b) $3 \le \sqrt{2x+5} < 6...
InequalitiesRadicalsAlgebraic Manipulation
2025/5/11
The problem asks to show that $x - 2i$ is a factor of the polynomial $f(x) = x^4 + 6x + 8$.
PolynomialsComplex NumbersFactor TheoremRoots of Polynomials
2025/5/11
The image displays the text "Algebraic Expression". There is no actual algebraic expression to solve...
Algebraic ExpressionsDefinition
2025/5/11
We are given the equation $\frac{x}{1+i} - \frac{y}{2+i} = \frac{1-5i}{3-2i}$ We are asked to solve ...
Complex NumbersLinear EquationsSystems of Equations
2025/5/11
Solve the equation $\frac{x}{1+i} - \frac{4}{2-i} = \frac{1-5i}{3-2i}$ for $x$.
Complex NumbersComplex Number ArithmeticEquation Solving
2025/5/11
We are given the equation $\frac{1}{x+iy} + \frac{1}{1+3i} = 1$ and we need to solve for $x$ and $y$...
Complex NumbersComplex Number ArithmeticEquation Solving
2025/5/11
We are asked to solve the equation $x^{\frac{2}{3}} + x^{\frac{2}{3}} - 6 = 0$ for $x$.
EquationsExponentsRadicalsSolving Equations
2025/5/11
The problem asks us to solve the inequality $|\frac{x-2}{x+3}| < 4$.
InequalitiesAbsolute ValueRational ExpressionsInterval Notation
2025/5/11