Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We are given the expression $ax^3 - x^2 + bx - 1$. When this expression is divided by $x+2$, the rem...

Polynomial Remainder TheoremPolynomial DivisionLinear EquationsSolving for Coefficients

The problem asks us to find the values of $a$ and $b$ in the expression $ax^3 - x^2 + bx - 1$, given...

PolynomialsRemainder TheoremSystem of EquationsCubic Polynomials

We are given the expression $ax^3 - x^2 + bx - 1$. When this expression is divided by $x+2$ and $x-3...

PolynomialsRemainder TheoremSolving EquationsAlgebraic Manipulation

We are given two equations: $9a + b = 29$ $4a + b = -14$ We are asked to solve for $a$.

Linear EquationsSystems of EquationsSolving for a variable

We are asked to simplify the complex number expression: $0.5i^{12} + \frac{(3i+1)(i-3)}{i-1}$.

Complex NumbersSimplificationArithmetic of Complex Numbers

We need to solve the equation $3 \cdot 3^{x+1} = 27$ for $x$.

ExponentsEquationsSolving for xExponential Equations

We are asked to solve the equation $5^{2x+1} = 125$ for the value of $x$.

ExponentsEquationsSolving Equations

We are given two conditions relating two numbers $x$ and $y$. First, their sum is 35, so $x + y = 35...

Systems of EquationsLinear EquationsSolving EquationsSubstitution

The problem is to solve the following system of linear equations for $x$ and $y$: $6x + 4y = 7000$ $...

Linear EquationsSystems of EquationsElimination MethodAlgebraic Manipulation

We are given the function $f(x) = x + x^2 + x^5$ and asked to determine whether it is even, odd, or ...

Function PropertiesEven and Odd FunctionsPolynomial Functions

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