Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
We are given the polynomial $P(x) = 4x^3 - 4x + 1$. We want to find the remainder when $P(x)$ is div...
PolynomialsRemainder TheoremPolynomial Division
2025/3/20
The problem asks us to add three polynomials: $(x^2 + 8x - 7) + (-4x^2 - 2x + 1) + (x^2 - x - 2)$. W...
PolynomialsSimplificationCombining Like Terms
2025/3/20
We are given the polynomial function $h(x) = 2x^4 - x^3 + 2x^2 - 6x - 5$, and we are asked to evalua...
Polynomial EvaluationPolynomials
2025/3/20
We need to solve three separate problems: 1. Solve the logarithmic equation $\log_2 x + \log_x 4 = 3...
Logarithmic EquationsExponential EquationsRadicalsSimplificationChange of BaseQuadratic EquationsRationalization
2025/3/20
The problem asks to solve the logarithmic equation $\log_2{x} + \log_x{4} = 3$.
LogarithmsChange of BaseQuadratic EquationsSolving Equations
2025/3/20
The problem asks to express $\frac{3\sqrt{2} - \sqrt{3}}{2\sqrt{3} - \sqrt{2}}$ in the form $\frac{\...
RadicalsRationalizationSimplificationAlgebraic Manipulation
2025/3/20
We are asked to express $\frac{3\sqrt{2}-\sqrt{3}}{2\sqrt{3}-\sqrt{2}}$ in the form $\frac{\sqrt{m}}...
SimplificationRadicalsRationalizationExponents
2025/3/20
We are given the expression for $y'(x)$ and are asked to simplify it. The expression is $y'(x) = \fr...
Algebraic SimplificationExponentsRational ExpressionsDifferentiation (Implied)
2025/3/20
The problem states that $y$ varies directly as $x$ and inversely as $z$. Given that $y=4$ when $x=8$...
Direct VariationInverse VariationProportionalityVariablesConstants
2025/3/20
The problem states that $y$ varies directly as $2x$ and inversely as $z^2$. We are given $y=4$ when ...
Direct VariationInverse VariationProportionalityAlgebraic Equations
2025/3/20